Many patients feel like polishing is what’s actually cleaning their teeth, not the instrumentation, so I see where your patients are coming from. It is important to polish all surfaces, but you must do so with the correct polishing agent. When polishing crowns and veneers you don’t want to use a paste that has abrasives like regular prophy paste due to micro scratches (like you mentioned). Many dental companies make such paste, talk to your dental rep to find a good choice for your office and perhaps do some research online to familiarize yourself with these products. I polish crowns and veneers first with crown-specific paste then polish the remaining teeth with prophy paste, with the correct grit (fine, medium, coarse) depending on stain, biofilm, etc. If ordering crown/veneer paste is out of the question (your doctor says no) then the next best option may be to polish crowns/veneers first without any paste then do the rest in prophy paste.
 
This is also a good time to educate your patients that you don’t want to damage their expensive crowns and cause scratches that can harbor bacteria, which is why you are using different paste (or no paste). If they ask why the last hygienist didn’t do it this way, explain that as new research emerges, better protocols come about. Don’t say that the last hygienist wasn’t up to date with the newest protocols or anything like that.
 
Another thing I’d like to point out is that it sounds like your school taught you “selective polishing” technique. The newest standard of care is “essential selective polishing” technique. Here’s an article that explains the concept well: http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1011&context=dentistryfacpub