My character attends military academy so gets all the service skills at 0. At graduation, the character gets to increase three skills to 1.
Not quite, and that's exactly what's messing you up for your following question.
Your character attends military academy and gets all the service skills at 0.
Done, that's all you get.
Except for graduation benefits, which are +1 Edu, a chance of +1 Soc if graduating with honors, automatic entry into the service, and an early roll for commission at +2 so you can enter as an officer. So really that's still a decent first term overall, but for skills that's all you get.
... what skills does the character get for the first term in their chosen military career if they'd gone to the academy?
Now is when you get to select those three service skills at 0 and raise them to 1. Then you make a further roll for promotion, and may gain another roll if that's successful as normal.
page 15 said:
If entering the same military career the academy is tied to, select any three Service Skills and increase them to level 1.
Emphasis mine, but the key here is just reading it literally. If you didn't enter the same military career the academy is tied to you wouldn't get them at all. Except it happens to appear in the list of Graduation Benefits rather than as a separate second step, which throws people off, but the plain reading is pretty clear.
Now whether everybody likes it this way or house rules it to work differently is another question, but this is the by the book answer.
I think it actually is more or less balanced. It comes out equal to rolling twice in your first term and once in your second, but taking all rolls on Service Skills and happening not to get any repeats. It's just that getting them all in one lump sum instead of spread out leaves people trying to shoehorn something else in where the individual rolls would have been.