Yeah you're right it can be all corn, but all the bourbons I know of, save Tuthilltown, have some rye, wheat (Makers), and barley malt for conversion. The all corn ones usually say 'corn whiskey' or 'spirits distilled from corn' if it's white dog. Charring the barrels allows for some filtering to occur. If the grist is all corn, you'd have to use added enzyme or malt the corn, which, because malted corn doesn't have much enzyme, means that all the corn must be malted. I don't know if there is a minimum age requirement, but probably not as THT is only a few months....
It's really just semantics I suppose.