Yes it's a common misconception, offiically military press is feet together standing - this means that there's much less chance of you leaning back to compensate for the weight.
however over the years standard shoulder press has now been dubbed "military" press - incorrectly I might add.
Seated shoulder press should also be done without the back rest for true representation - otherwise most people arch their backs and push against the the backrest which is cheating somewhat. I can add a good 20kg to my lift with the backrest up.
Having the backrest up has it's place of course
As for paritals, they are good for punching through sticking points and activating the connecting tissues in the muscles and tendons that are struggling - so yes, in a way they can help strength as once you've pushed through that sticking point you may be able to lift more.
My sticking point on bench for example is around 3 inches from my chest so what I could do is load the bar up on a rack at exactly that height and practice lifting it from that point again and again and again and it'll only come down as far as the rest stops.
However, it, in itself, does NOT increase strength - it helps the weaker part of your ROM... if they were not concentrating on their weak point (i.e. like my 3 inch from chest area) and just doing it for the sake of getting "stronger" then I very much doubt it.
For a start it'll impair their flexibility, tighten the muscle group and make it such that it may actually weaken their full ROM as a result.
Partials should only be used for sticking points, or in combination with FULL ROMs to aid explosive/power development. Partials alone are pointless.