I have been told by an employee that they don't like rekeying your lock because it takes the business away from locksmiths. Does that make sense?

Home Depot's core business isn't being a service company, it's selling products. They'll do certain things, but mostly I think it's subcontracted, so they don't do everything. Sure, making it sound like they are looking out for the little guy sounds like a nice thing, but I doubt that's the reason.

I've never heard of this??

No, ask for Store supervisor

Nope

No