Well, in "The Breach" (ENT), Phlox said they were "prodigious" breeders, not specifically fast.
Also, much may hinge on Edward's emphasis of "this particular species" in his comments here. Perhaps meaty-but-slow-to-multiply-and-easily-harmed Tribleustes ventricosus is a dying breed on Iota Geminorum IV, being rapidly or gradually crowded out by Polygeminus grex and any number of other varieties—cf. ants, frogs, et al.—and falling victim to the very same abundance of predators that the latter evolved their quicker and/or more robust reproductive capabilities as a survival mechanism against in the first place?
Could be.
Remember, Larkin both has a specific agenda...and is an idiot. (Who knows if the cause to which he shruggingly ascribes the effect observed—what else but the contribution of his own DNA—is even the true one)
Meta-wise, I don't think we're supposed to believe he's wrong.
Further, recall what happened to Cyrano Jones when he tried to have his small-but-fast-breeding tribbles genetically tinkered with in an effort to stop them from reproducing in "More Tribbles, More Troubles" (TAS)...he (temporarily) wound up with super-extra-meaty ones!
Weird alien shit be weird.
Sort of; the "giant" tribbles were just regular, sterile tribbles clustering together (how so many ended up on the ship when Jones only beamed up with a few is another question).