Well, maybe, assuming he has weapon focuses or whatnot -- which isn't guranteed, he could just as well be a pally or a ranger or something and lack the necessary feats.
However, that's not the point. The point is that a guy who has no logical reason to have trained with a rapier is proficient with it. I'm all for fighters having a broader weapon knowledge than others, but "all martial weapons" is a little too broad.
It's not THAT bad. You aim for four or five weapons in each group and one or two exotics.
For example:
Axes (Throwing axe, Handaxe, Battleaxe, Greataxe, Dwarven Waraxe)
Polearms (Spear, Halberd, Guisarme, Ranseur, Glaive)
Hammers & Picks, AKA "Impact" (light hammer, warhammer, light pick, heavy pick)
Swords (scimitar, falchion, longsword, bastardsword, and greatsword)
Light blades (rapier, shortsword, dagger, kukri)
And so on.
It may take a little work, but it's hardly "fiendishly difficult".