It would require probably hundreds of thousands of dollars of extra salary before I would consider sharing that info with my employer, possibly millions (not exaggerating). Trading that info even for tens of thousands of dollars (let alone peanuts like gift cards) seems deeply unappealing to me.
If they needed a digital version of a doctor’s sign off, that’s enough for me to say no thanks. I don’t want them knowing when or where or how frequently I check off their particular health checklist items. Giving them any more details, such as the result of tests, would be an astronomical violation of trust, no way.
I even hate it that my insurance company generates paper _or_ digital records stating the exact application of my benefits (resulting in a copay, etc) for individual appointments, even if I already paid the relevant bill onsite at the doctor.
It just creates a data exfil / hacking risk if it’s digital, or a risk someone (China) will pick through trash or recycling and get it, when there’s literally no need to create the record (they’d already have the claims record from the doctor making a claim, this is a separate thing they generate to send to me redundantly describing the applied benefits... note: it’s not a bill (and very clearly says it’s not)).