If you're getting only 2 or 3K RMB per month, I think that's seriously robbery, even if you do have the ability to claim expenses on everything else. That's what only new graduates get, and low-level Chinese university new grads at that. I have a friend who just moved from IBM to Microsoft recently (we're both in China). Microsoft definitely pays more than that. I have no idea where you're getting this 2 or 3K number?
To the gp, I usually don't get fapiao if I don't ask for it, but it sometimes comes. I always get it if I ask for it, or they offer me a Pepsi on the house or something to avoid giving me fapiao. So it's always in play, as far as I can see.