How America views treaties and agreements.
It would be the height of folly to exchange anything tangible for a paper promise from the Americans.
America dropping threats today is meaningless as they can just make even more outrageous threats tomorrow once they got what they wanted from you.
That is why China should only provide assistance which aims to create conditions in which yes, American economy may be improved, but China's economy will benefit from it as much or even more.
No nation can thrive solely off foreign aid. If that was the case, Africa would be the richest continent, not Asia.
Foreign aid can kick start America again if Americans are smart about it. But I'd say that is a risk China can take. Giving these types of aid will not weaken Beijing, on the contrary, the movement of goods will provide orders, expand businesses at home.
Making Americans tear up their invasion plans in public is worth such a price, if only to humiliate them for even considering it in the first place as well as giving China more time to enjoy peace dividends and continue its porcupine strategy.
Even if they can eventually do the threats again, so what? The power balance will be even worse for them at that time.
I think China should fish for a deal, as long as the deal provides signficant concessions at least in the short and medium term.