Chinese folks being weary of restaurants with swapping ingredients for lower tier is not comparable to assuming chicken being swapped for cat, which is a tired joke. Usually reserved for pricer seafood, hence pick your victim tanks. Many restaurants do similar type of substitute shenangians, like I'm pretty sure the hipster burger joing is not serving genuine kobe beef patty for $15, but they're also not serving ground chihuahua either. Like even in PRC you're worried about things like gutter oil at a hole in a wall joint versus slightly cheaper grade of sea cucumber at a fancy restaurant. Even during the pork crisis, no one was particularly concerned that restaurants were feeding them cat/dogs instead.
E: relate back to your parent comment, there's somethigns like cultural appropriation that most (especially older gen) Chinese don't care about, i.e. they thumbs up for white girls wearing qipao.
https://www.usatoday.com/story/news/nation/2013/02/20/fish-s...
https://projects.tampabay.com/projects/2016/food/farm-to-fab...
I don't know the right answer, but I definitely think it would be understandable if someone didn't appreciate that joke. And worst of all, it's just in service of the cheapest, blandest kind of humor. The writers should be ashamed of such lazy work, regardless of bigger issues. "Would it work without a laugh track" clearly fails badly here, as it does pretty frequently in TBBT.
FWIW I have a few data points -- this is something my Chinese wife has literally said inside a Chinese restaurant, and some of her other family members have said similar things about not trusting that the food being served is what they said it was.