Disc brake rub problem
Check that the rotor is true. If the rub occurs at a specific point of wheel rotation the rotor may be slightly bent. You won't be able to adjust the caliper position to eliminate rub if this is the case. 

Rub is not caused by the pistons being advanced too much, so there is no point pushing the pistons in. As soon as you use the brakes they advance again. However, a piston might be sticking, so that it is not retracting from the rotor when the lever is released. You can try to unstick a piston by carefully advancing an cleaning it.

These Park Tool videos may help you: