Any doctor who doesn't know prednisone can cause hair growth sure as heck shouldn't be scripting it!!! Or is one of "those" doctors full of platitudes who will tell you ANYTHING to get you to do what he wants you to do, i.e. take the pred and ignore the new hair growth. And who can trust a doctor guilty of either?
I'm the stubborn type. I'd bring in the drug literature to PROVE that pred can cause hair growth and clear the air w/the doctor; was he/she really not aware of this possible, even likely, side effect or was he/she being evasive or condescending to me? I'd also make it clear I am uneasy w/a doctor who is unable to say "I don't know" or just mumbles whatever he/she thinks necessary to get me to do what he/she wants me to do.
That clears the air and either the two of you then have a better understanding of each other and work better together as a team or you start looking for a doctor whose advice and answers are more reliable and trustworthy.