I can’t see why they would be entitled to see your complete medical history! It is reasonable for them to want evidence of your diagnosis, as it confers special rights under disability legislation, so they’re entitled to satisfy themselves you do actually have those rights, and it’s not something you’ve made up.
I can’t see why they’d want or need to know about unrelated stuff from years ago, if that’s what you’re worried about - it’s not going to come up!
Have there been any issues about attendance and/or performance? If not, they may just be wanting to cover themselves, by checking with your doctor that it’s SAFE for you to continue working, and that there isn’t anything they shouldn’t be allowing you to do. I think that’s reasonable, and not sinister - they want to protect you - and themselves - from you claiming later that you were unreasonably forced to do something a person with MS shouldn’t have been doing, and that they didn’t look after your welfare.
I don’t think it’s anything to be worried about - I think they’re just playing it safe. They want to know about any special needs or limitations, so they can be appropriately handled.