One of those reports suggests heat and change of drugs. Not that early for dementia - he's 80.
I sang with a couple of JEG's English Baroque Soloists/Monteverdi Choir in the Bach choral course I attended in St. Andrews. One of them, Sam Evans, was the Course Director. The other was Katherine Fuge, a soprano, who came as a visiting lecturer and singing coach. Neither of them suggested anything unpleasant about him other than the massively demanding standards of one of the top musicians of his age. But then of course that's exactly what one would expect. One session involved a question-and-answer session with Katherine and she was asked about working with him.
He's quite an unusual musician in that so far as I can tell he's not outstandingly proficient on any instrument or with his voice, but just grew up as a conductor. He's widely regarded as the pioneer of playing ancient works on period instruments.
Wikipedia says this:
Gardiner has been the subject of various allegations of rudeness and bullying of performers and colleagues.
with three referring links to citations, at least one of which is defunct. Another is
here.