Wheelchair is not covered by Medicare going from SNF to LTC?

Ok...this makes no sense to me. But I’m wondering if there is a way around it.
Dad lives at a continuing care center that has all levels of care under one roof. He lives in AL, but fell and went to the SNF there for rehab. He is being discharged directly from SNF/rehab to LTC where he will now live. I asked for them to do the Medicare paperwork for a wheelchair since the doctor and therapy said he needs it. Yesterday the director said Medicare won’t pay for a wheelchair for him because this LTC doesn’t take Medicaid and therefore since it’s private pay only, they won’t pay for a wheelchair. That just sounds crazy to me. She said it’s a Medicare ruling. WTH??? Does anyone here come up against that and is there a work around. I realize wheelchairs aren’t that much and he can afford it but this sounds nuts. But then that’s Medicare for you.