Ah, I need to edit what I wrote above. That was incorrect.
When it says, "soldier+1+ammunition", what it means is "perform a soldier check at +1 but spend an ammunition". It is not specifying that the crew member must be trained in the soldier skill; it's just telling you what type of check you're making. (This is different than what I wrote above which was incorrect. Sorry; an earlier setup of the game split out attacks by soldier/non-soldier, but it was replaced by just giving soldier-trained crew a roll bonus. This is cleaner.)
Every crew member may attempt a soldier check. It's just that the ones trained in it get a bonus on the roll, so they're more likely to succeed when they do.
So any crew member can take advantage of that method to attack (assuming they have the ammunition to spend on it). It's just that when they do so, solider-trained crew have a +3 on their roll, while non-soldier-trained crew have only a +1 on their roll.
This distinction is important in case all your soldier-trained crew have been killed or are otherwise unavailable in the fight. It is entirely possible, especially in the late game, that no one on the crew will have a given skill. They still need to be able to fight!
Sorry for the confusion!