I don't think you're missing anything and I certainly didn't mean to imply that you were doing anything wrong.
And if the customer balks at the photocopy then the tellers can simply note the information on a piece of paper, which of course follows the same trail as the photo copy would. If the customer doesn't want to provide his ID and SSN, one way or another, he is welcome to go down the street.
We're talking about non-customers though, right? In the case of an employee making a deposit on behalf of his employer, he does not have the option of going down the street to another bank. Obviously that's different than someone trying to cash a check and objecting to giving personal info. An employee on an errand can't really do that.
I'm just saying that, in light of all the "identity theft" and privacy scares out there, I would be uncomfortable, while making a transaction on behalf of my employer, letting a random teller make photocopies of my personal information. Especially if I was more than cooperative and gave her my personal info to fill out the CTR. I've had to do that numerous times and never had a problem. I would draw the line though at the teller taking my SSN card and DL and going to a photocopy machine in the backroom to make copies.
I am just playing devil's advocate here, that's all.