There's natural curiousity and there's prying which is the modus operandi of a nosey parker.
There's the natural curiousity of a landlord borne of concern for their property which may lead them to check out prospective tenants by other means than written references but which, taken to extreme, becomes prying.
He has overstepped the mark with FB and alleging that he couldn't find the lad when you were able to access his profile without any problem gives rise to suspicion that his motivation wasn't to make additional checks out of concern for your property, but was something considerably less wholesome, i.e perving over photos of young women.
If he cannot see this, and cannot see how disrespectful it was to make these searches without informing or including you - after all, you found the guy and could have easily found the gals if he'd said 'let's take a peek at FB to check these prospective/signed tenants are who they claim to be' - there isn't much hope he'll change his ways.
That's not to say that the pair of you should be joined at the hip unable to act independently of each other but, when it comes to matters in which you have a joint vested interest, there shouldn't be any secrecy in either of your dealings.
And if he's going to continue to be secretive about these matters, he's got to accept that, in common with any rightminded person, you may become suspicious and fear the worst about why he's being secretive.
I feel like I'm going round in circles here and it's irritating the shit out of me, so god knows what you feel like having to deal with this on a regular basis, dolly 
Regardless of whether he was perving, he's a silly sod to risk so much for the cheap thrill of spying/prying into your tenants' private lives and he should know that being a nosey parker is not a trait that wins universal acclaim and approbation - it's a character defect which he's best advised to address before someone punches him on the nose takes exception to his behaviour.