> Turning down gifts sends a strong social signal that you don't want whatever relationship the gift implies.
I believe that interpretation is incorrect.
In Chinese culture, it is important to balance social relationship, and the worst is to own someone favor. Owning some others favor means to repay the favor at some point; and you can't simply repay the equal favor later, you have to do something more significant to truly balance -- in fact, I don't think in Chinese culture, a favor can truly be repaid -- therefore, to accept a favor is truly a (lifelong) commitment. With such context, you would not want to accept a gifts easily, you would honestly would like to decline the gift (while noting down the gift givers gracious -- yes, it is all about the gesture). Also the attempt of declining downplays the favor (as the gift is not truly great favor as I could decline it).
In Chinese culture, there is a strong concept of social obligation (balance).
So Chinese do want friendship as in the intention of gift giving in a western culture, but most Chinese would rather other people owning to their favor rather than the other way around -- and Chinese do keep count -- unless the relationship is so close that there is no need to keep count any more; but then exchange gifts at such level is also absurd.
Of course when you don't want the relationship, then you absolutely don't want to accept the gifts.
PS: Actually this is how Chinese corruption works. You try hard to bribe officials with some gifts or dinner even when the official would not value your gifts at all (because he already had too much), but as long as the official accepts your gift (often because you are so sneaky that he cannot easily return your gift), then this official is obligated to help you out (often means to go out of his way). First time is always hard, but second time is much easier.
And that is why to be a Chinese official is difficult, you abide by the rule, then you become socially cold and judged down in culture; or you could be generous accepting bribes and doing favors for everyone -- you become popular, but on the other hand, you have some crimes that some day will become your downfall -- not because of law, but because of power shift (which is inevitable). Greed is just the byproduct.