I wouldn't say that Tom, wouldn't want to put my name and numbers to a plane had someone turning wrenches on it in secret, if it's logged you could always double check the work if you were concerned.
IMHO I don't keep secrets from my APIA, personal or aircraft logs, and I'd expect my APIA to not do undocumented work ether.
I suspect Tom was meaning that Dr. O should find a mechanic who's work is better than his. At least that's how I took it.
I agree with you and the others that would not want to sign off on someone's airplane when you have no idea what the owner did to it because they refuse to document their work. There are a number of those guys locally, some of whom think that if they tell me about what they're doing that it constitutes an approval. I will not sign off on their stuff, because I have no idea what they actually did or how they did it. There seems to be no shortage of mechanics who will sign their stuff off though, so I just might be too conservative.