Used to do a lot of hot-forging of titanium, which isn't exactly dental, but:
Titanium metal generally has a passivized transparent oxide layer in atmosphere, it's why you can draw a full range of anodization colours with a flame- light bounces around inside that oxide layer, and the depth of it determines the visual wavelength and therefore the colour perceived. You won't get black with that non-electrochemical passivized oxide layer, it maxes out at a deep, dull brown.
As I understand it, there are a range of processes to blacken titanium deliberately, but they're proprietary electrochemical anodizing processes, or else chemical processes that are incompatible with the human mouth, i.e. something that starts with submersion in chromic acid at 160C and gets nastier from there. But there are a lot of weird techniques I've heard of people trying, most of them giving inconsistent results. Lots of bladesmiths trying to blacken titanium scales for knife handles and the like. You won't find a good, consistent blackening technique that's suitable for mass-production in public discussion, because all the finishing houses that have worked something out keep it as a guarded trade secret. Or that was the state of things a decade ago, how time flies.
I agree that it's probably a cleaning solution reaction. Find out what the patient is using- my gut-impulse guess is something to do with fluoride compounds from toothpaste/mouthwash, but that isn't based on much.