Somebody please parse the error in this sentence

From The Atlantic on mozzarella di bufala versus the regular cows' milk stuff: Buffalo milk connotes luxury, but aside from its much higher butterfat content, it doesn’t necessarily taste better.

I'm having a lot of trouble interpreting what this sentence is saying. First of all: "Buffalo milk connotes..." Puzzlement follows.

Second: "aside from... it doesn’t necessarily..." Is this an admission that higher butterfat content is a sufficient condition for greater deliciousness? If so I have no quarrel. But then the author dismissively and in apparent self-contradiction suggests "it doesn't necessarily taste better." So, higher butterfat is neither necessary (since other qualities can make something more delicious) nor sufficient (since even something with higher butterfat can in fact not be more delicious). But the latter assertion conflicts with what we know about the world. So I just don't understand.

Bonus points: False dichotomy! (Bufala v. regular: often taken to be a difference of degree not kind, delimited by a socially agreed or bureaucratically imposed norm.)

Happy Christmas.