It's not, but "seeing multiple doctors and getting different opinions opiates IS illegal.
So is "doctor shopping" seeing multiple doctors at the same time while getting different opiates from said doctors?
Or is "doctor shopping" seeing multiple doctors at the same time while getting the same opiates from said doctors?
Or is "doctor shopping" seeing multiple doctors at different times while getting different opiates from said doctors?
Or is "doctor shopping" seeing multiple doctors at different times while getting the same opiates from said doctors?
I can see it being illegal if Rush was seeing multiple doctors at the same time and getting the same or different controlled drugs without informing said doctors of other prescriptions, which might indicate he was building a stockpile for his addiction.
However, the above is pure speculation. I'd like to see the exact "drug shopping" law in question.