With this p-code and the symptoms you describe, the most common problem is going to be the rear wheel speed sensor located on top of the rear differential. This sensor is where the PCM reads the speed from, and when faulty will set a Brake and ABS light.
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Hmmm. That's odd. Tell you what, let me opt-out and forward you to another Tech that may have a better idea as to what's going on here. Sit tight one sec, someone will be right with you...
Hello my name is XXXXX XXXXX X will take a shot at this. The ABS controller may have failed. Do you have a scan tool that can communicate with the ABS controller?
Ok, that is fine, but what I would like to know is if the mechanics were able to communicate with the ABS controller. Not the PCM (engine computer). You see if the ABS controller is not working, then the PCM will not get a speed signal from the ABS controller. This would cause that P0501 code to be set in the PCM. So we need to check that next.
Ok, sounds good. Let me know how it goes,