Some discretion has to be used, of course. Profession and Science, which have any number of specialities, are two skills that wouldn’t give a level zero skillset to all other specialities. For example, Profession (Finance) 2 may also grant Profession (Accounting) 0, but it wouldnt grant Profession (Civil Engineering) 0. Science (Chemistry) 3 should grant Science Science (Biology) 0, but does not imply Science (Planetology) 0. Some common sense, and ultimately, referee fiat, has to apply here.
I would also as a referee, if asked, grant Science (Biology) 0 and Science (Chemistry) 0 or maybe even level 1 to someone with Medic 3, just thinking of the rigors of medical training. I’m sure there are other good examples.
I don’t think I’d agree with a broad Starship skill, at least not without a high level required that would increase the complication of the game. To use a real life example, I’d like to think I am a Driver (wheeled) 1. Although everyone thinks they are better drivers than they actually are, so maybe I’m really Driver 0. Either way, that may also give me Driver (Tracked) 0, but it certainly doesn't give me Mechanic 0 ( or give my wife Navigation 0
). And starships are much more complicated than automobiles. Docking a starship, fixing a jump drive, and plotting a course through the stars are very different skills. Maybe Driver (wheeled) 3, which to me would be a top notch race or stunt car driver, also requires Mechanic 0. That’s pretty reasonable. Up to you if you want to add these details to your game. Last one: should Gun Combat (Slug) 3 give a traveller something better for a laser rifle than Gun Combat (Energy) 0? They aim the same way, don’t they? Of course, firing a gun with significant recoil on target could be much harder than a gun with Zero G, i.e. limited or no recoil.