No, there are several pre-career options which allow you to roll life events. Just like you may get the full slate of skills from Basic Training if you do University in your first 'term', because 'University' is not a career.
There is only one pre-career event that allows for psionic training (a roll of "2" on the table). Rolling that event would in fact allow you to take Psion as your first career, but I think whether you get full Basic Training in the Psion career depends on how you got there.
Yes, I agree that University does not count as a separate career, so you would receive full Psion Basic Training in your next term as it is "your first career". This is how University functions with
all careers - your first term after you graduate is your "first career" and you receive full Basic Training for it. University does count as a term served for purposes of determining PSI, though, so the roll will be 2D-1.
Colonial Upbringing from the
Companion acts the same as University for Basic Training purposes (you receive full Basic Training in your first term) but it counts as
2 terms served for determining PSI, because a player with Colonial Upbringing is age 22+2D3 (24-28) before beginning his first career. That's the price you pay for all the additional skills Colonial Upbringing grants.
The Military Academies provide Basic Training as part of their curriculum. So if you go to a Military Academy then you don't get Basic Training in your first regular term of your military career - you already received it at the Academy. Your first term in a military career gets you the normal one skill roll/term (plus any gained by commission, advancement, or events) instead.
If you go to a Military Academy and roll the pre-career event that gets you psionic testing and then go on to Psion as your first career instead of the military career you had planned, then for purposes of Basic Training the Military Academy
does count as your first career, and you receive one level-0 skill as Basic Training in the Psion career. It also counts as a term served for determining PSI.
Same story with the Merchant Academy from the
Companion. It already provides Basic Training in the Merchant career, so Psion would count as the second career for Basic Training purposes.
Psionic Community from the
Companion counts as having received Basic Training for the Psion career. If you have the Psionic Community background you don't get any basic training in Psion - you get the normal one skill roll for your first term (plus any gained for advancement or events). This is the only way into the Psion career that allows you to determine PSI with no terms served for Imperial humans.
I think this incorrect; the 'Life Sense' power (as just one example) is not a skill separate from Telepathy -- anyone who learns Telepathy can usually attempt the 'Life Sense' power. Aside from odd events, the way to improve your chances of using a power is entirely due to increasing levels in the Talent. 'No Talent' means no access to the powers in that Talent, not 'use the power at -3 for unskilled use'.
The rules are a bit ambiguous as to whether
psionic talents and
psionic skills are distinct from each other. Sometimes it's pretty clear they are, and other times less clear.
"If a Traveller learns a
talent, they gain it at
skill level 0".
"There are several psionic
talents, each of which is controlled by a different
skill." That one seems pretty clear, but also conflicts a bit with the first quote.
"To activate a power, the Traveller must make a
skill check using the appropriate
skill (Telepathy, Telekinesis, and so on)."
"When rolling on the Service Skills table, if the Psion gains the
skill for a
talent they do not yet possess, they may attempt another roll to learn that
talent."
I think it makes the most sense to treat Talents and Skills as separate.
In every instance if you learn the Talent you get the associated skill at level-0. So no, there are never any "unskilled" psionic power users that would have the -3 for unskilled use penalty. But if a Traveller had to make a skill roll to know "what sort of things can you do with Telepathy?" that roll
could be made unskilled.
If a Traveller never learned the Talent but gained a psionic skill then I don't let them use any of the powers, even if they have other psionic talents. Likewise, I let PSI 0 individuals learn the skills without being able to use the powers.
I'm not sure that is correct, nor whether it has been clarified at all. The skills obtained in Basic Training are specified as 'gain skill-0', which supports the idea, but the skills listed on the Service Skills and Specialist Skills tables do NOT specify skill-0. This seems like a thing that could go either way; as a referee (in my own Traveller Universe) if a player had already skill-0 all six skills on the appropriate table, then I would feel bad about screwing them out of the Basic Training term & just let them take a regular skill roll for the term.
As far as I know it hasn't ever been clarified.
I read Basic Training as just that - a broad basic course in all the basic skills needed for the profession. It
can't teach a Traveller beyond level-0 competency. Smart players in my games don't pick Background Skills that they expect to learn in Basic Training for their first career.
Second (and additional) careers provide only one level-0 skill for their basic training because they don't provide a broad basic competency course to people who have already been in the workforce for a while. The level-0 skill they get represents the abbreviated training they get while performing their normal duties. It might feel like screwing the player out of a full skill level, but the 0-level skill does still have the benefit of being a skill of the player's choice rather than a randomly rolled skill.
The skills on the table for each career do not specify skill-0 because if they did they wouldn't provide any benefit after Basic Training during regular terms served.
I am fairly sure that the Talents gained in Basic Training do not require rolls to test whether or not they are learned; if a Psion chooses a particular Talent from Basic Training then they get it without a roll or any chance of failure.
That reading would mean that all Psions who had Psion as their first career automatically receive three psionic talents (two if they're a Wild Talent) with no rolls necessary to acquire them.
A player could game the system by attempting to learn only the Telekinesis and Clairvoyance talents when generating his PSI (when done in that order both rolls are at +2), then taking Psi-Warrior as his first career to automatically gain Telepathy, Teleportation, and Awareness from Basic Training. He only has to be reasonably lucky (with a PSI 6-8 he only has to make three 6+ rolls - two to learn the talents and one to qualify for the career. If he has PSI 9-12 they're all 5+ rolls) to end up with
all five psionic talents at the end of his first term.
If he failed to learn Telekinesis or Clairvoyance he can make all his skill rolls on the Service Skills table hoping for the talent he's missing or the "Any Talent" roll and try to learn the talent he's lacking with only a -2 DM to his roll (because this is only the
third talent acquisition
check he's made, even though he already has three or four other psionic talents).
Someone who isn't taking Psion as their first career would still automatically end up with two psionic talents, with a very good possibility of three. Take Telepathy as his first talent in training so he gets it automatically, roll for Clairvoyance at +3 (since he didn't have to make a check to get Telepathy this is his first
check), and then learn a third talent automatically as part of Basic Training. He has a fairly good chance to learn a fourth talent during character generation as well.
Since the psionic rules seem to be set up to make such multiple-talent Psions very rare, your reading seems too powerful to me. I will go with the "make another attempt to learn the talent or take a level in the skill without learning the talent" reading.
Two more side notes:
I do not allow Travellers to select a psionic skill with the Connections rule unless they already have the skill and are just improving it a level.
If a Traveller is already a Psion I let them re-roll the Life Event that grants a chance for psionic testing and training.