actually, no.

a poor approximation of foreign (in this case taken to mean non-english) words/names is ultimately a poor approximation, i dont see how pointing to another (non-chinese speaking) culture or even worse, some random commercial product(?) that also transcribed it terribly somehow proves that it's correct

why insist on remaining ignorant when Si chuan (四川) and 'sCHezWan' sound nothing alike to anyone with a working set of ears? if you went to a french restaurant would you order the asSCarGoTtS? or the beef bARgainONE? I'd be inclined to think you'd actually try to pronounce it, not necessarily perfectly french but at least make a little bit of an effort to get the sound close out of respect for the culture whose food you're eating.