Old discussion but here is my experience. Yes there is a kind of cheap MDF which is fluffy and generally very bad quality for work. I would say impossible.

Once i did 100 pieces , some lamp bases, for a friend and all was ok. Next time they bought the crappy material. OMG, it was a disaster.

Side by side before machining it was lighter in color and not so glossy as the real MDF. In short the best MDF i have found here in Spain is the darkest in color and the smoothest to the touch that gives you a glassy like feeling. And yes, from MDF to MDf there is a big difference even in one shop