Yeah, I think the argument essentially is, “They thought this is how you’re supposed to do it here.” Also that they didn’t actually know what was going on - the money they paid was to a non-profit, and they had no interaction with the person at Yale who was actually being bribed. (Certainly those are the kid’s arguments; apparently she didn’t even want to go to Yale but to Columbia, but she claims she thought she didn’t have a choice because of how college admissions worked here.)
From what I’ve read, there are two aspects to college admission in China. Everything, in theory, revolves around one test score, the gaokao, with higher scores determining whether one gets into one’s preferred universities. The scores are all made public, which prevents bribery. However, in order to maximize test scores, parents hire private teachers. Private teachers cost, per hour, about 2% of the average family’s annual wage, so it preferences the wealthy. Also there’s the second aspect - there’s apparently a regional quota for universities (that privilege areas where the ruling elite live), so students from the provinces, regardless of test scores, don’t have the same opportunities. (Then, of course, there’s the issues with biases in testing.) But this makes it one of the more merit-based systems in China (ironically, in this context).
They briefly tried allowing the individual universities to also have admissions tests and interviews (adding to the student’s gaokao score), but parents started bribing college officials, because every other aspect of Chinese interactions with officials is premised on some form of bribery or gift, due to systematic corruption and a tradition of gift giving.
It isn’t though, because of cultural differences. In China, bribes and gifts are an intrinsic part of the system. They may be, to various degrees, illegal, but they’re unavoidable. They’re an expected cost. Someone from China could plausibly have the misconception that some similar system of gift-giving was part of the US college system. Someone living in the US doesn’t reasonably have that expectation.
The fact that the US does have a University gift-giving system that privileges the children of parents who have a couple millions dollars to spend reinforces this division of understandings. The rich Americans were paying too little to take advantage of this accepted form of bribery (and they knew it), but the Chinese family weren’t. The distinction between acceptable and unacceptable bribes was erased by the amount of money being given.