I feel like the referral should come from their primary care preferably internal medicine.
I've noticed a pattern where Referrals to GIM from Rheumatologists tend to get denied more often. That can happen with other specialties as well.

I think with staffing what it is , that if they see you are already established with a specialty at home they are less likely to pick you up in GIM , and feel you should just refer to that specialty at Mayo perhaps.

Just my take on it from what Ive seen. A lot has changed since COVID and the availability and flexibility just isnt there.