Yes, not having QA is one of the ways unscrupulous businesses boost profits. The answer isn't to say “everyone in China is like that” any more than it was to say “every meat packer in the United States will serve you dog meat and pink slime” but to accept that some things need to cost more.
I would also note that in the case of that melamine incident 2 decades ago, several of the business leaders involved got death sentences which seems relevant to the question of how much the larger country supports it. For example, I note that no member of the Sackler family has failed to die rich out of prison.