How can side mirrors be painted?

Hi, I have some new side mirrors that I need to have painted. My body shop said that painting mirrors is really hard, since the actual mirror can't be removed. I bought aftermarket powered mirrors to replace my stock ones. He told me that they can paint them, but that they would only be able to paint as much as they could around the area where the mirror sits flush with the housing. Like whatever was surrounding the mirror, they could paint only what you could see. Is this correct? I don't think my shop wants to break the mirror, that's why they're saying this. Help me out, thanks.

-Shawn