I don't think 'weak, irrational' or 'nonsense' really captures the flavor of the statement, so if you'll please allow me to indulge myself, I'll take a stab at it:
How about: 'Irrational'?
Unless the genetic sciences have reached a point where we're able to build the genetic code one piece at a time for an organism the size of a horse, and considering that this is a 'clone' we're talking about (i.e., a perfect copy of a previous, 'natural-born' horse), then the animal in question is, indeed 'a quarter-horse', and and the aforementioned quote is, in fact completely irrational, inaccurate, and furthermore reeks of extreme butthurt. It's not like you can turn the poor animal upside down and find 'Made in {insert Asian country-of-origin}' stamped on it somewhere, if you get my drift, and they've misspelled the name 'quarter-horse' somehow, to avoid violating someone's copyright, it is in fact a quarter-horse and genetically indistinguishable from any other animal of it's particular breed. Would they get so pissy about it if it was an identical twin of another horse (does that happen with horses?)