I hadn't expected complaints that it's against canon, as the idea for it was lifted from a passage near the front of the Daemonhunters 40k codex.
Well, I may be mistaken, but the rule as I understood it was that daemonic possession destroyed the mind and soul of the possessed.
Knowing the passage in the start of the DH Codex, it is told by the former "possessed". Consider that if one is in the process of being possessed, I think they would care little about the specific completeness of such possession. (Also, even if they did care, they would be in no state to be accurate).
I personally read the passage as either an aversion of a possession or only partial possession (although I prefer the former concept) - if he were completely possessed (even if his mind were intact), he wouldn't be able to muster the control of his body to perform the "exorcism" as he describes.
In answer to your question, there are a great many ways to have a scarred, deranged Inquisitor.
If you want a similar answer perhaps his pride and arrogance lead him to get too close to a daemon he thought defeated, and is dealt a blow that delivers a daemonic venom
(that he fights as best he can - perhaps its effect is eventually halted with the aid of one of the Ecclesiarchy (potential option for a henchman here)), or perhaps something along the lines of Quixos getting a shard of daemon claw stuck in his heart.