There are several different "standards" used by the different manufacturers. The way the different devices identify "their" chargers is by the amount of resistance inserted by the charger across the data lines. In the case of our Nexus 7 (and the Sero 7), the data lines are shorted together. (This is why you can't charge and use the USB cable for other things at the same time. It's one or the other, not both at the same time.)
I have solved the problem for myself, by opening the charging cable, cutting the data lines, and shorting them together on the end that goes to the tablet. In my experience, the power lines are red and black while the data lines have been white and green. (HINT: Do not cut the power lines.) That could easily be different with different manufactures, so be careful if you decide to do this mod yourself. If you are not comfortable with soldering, I would suggest getting somebody else to do this for you.
After modifying the USB cable, the different chargers work fine, up to their rated capacity.