orderic vitalis mentions a certain physician (forgot
his name) who was a canon of Chartres, and who also
happened to be married and was not, apparently, a cleric
of any kind.

We need to be clear about our terms here (with due respect, Christopher).
The physician may not have been a "cleric" in the modern sense but if he was
a University-trained physician (as opposed to a barber-surgeon) then he was
definitely "Clericus" in the Neck-Verse, benefit-of-the-Clergy sense.

As I understand it, the post-Gregorian position was that a Canon could be in
Minor as opposed to Major Orders; a man in Minor Orders MIGHT marry BUT if a
Canon married he was expected to forfeit his prebend. Possibly where such a
canon had family influence his matrimonial status might be overlooked .....