I've had to use a work email confirmation (where they send a code/link) to get company-negotiated discounts/rates from Microsoft, Verizon, Lenovo, and other places, so I don't see a problem with it. Presumably this is in whatever contract they have, so it shouldn't be a violation of any company "personal email" restrictions as long as personal use of the code is allowed, as is usually the case.

I'd rather have them pre-verify my account than some vague notice about being asked for "proof" at the gate. On personal trips I don't usually have much with me -- I wouldn't have my badge unless on a business trip, and I last got business cards in 1994! I'd probably have to show the agent my work email account on my phone, which would be much more concerning privacy-wise than letting their backend system send an email. I do have a dog-eared "Emergency Contact" card with the company name somewhere in my wallet, for whatever that's worth.