As I previously asked - Would you ever, under ANY circumstances, ask for a picture of a non-relative boy/girl who was asking for a recommendation? Pulease! I have been asked for numerous references by my friends' teenage sons and daughters. It would never cross my mind, nor can I imagine would it cross yours, to ask for their picture. Who, besides pedophiles, do that? The answer is NOBODY!!
If I was running an acting and/or modeling agency, I would. "Send me your headshot and resume" is pretty standard in a case like that.