Not enough evidence to draw a conclusion from this... I am a very private person even though I have nothing to hide... I've always been a loner, so it's nice to have little things that are kept to myself.
Cheaters become more emboldened over time and eventually reckless... even without snooping, you'll begin to notice changes in their behavior that would clue you in. Also, if you no longer trust the person, then you might as well throw in the towel. Relationships need trust... or else you just have a set of lies and routines.
Take this as being innocent until proven guilty. If he is cheating... sooner or later, he'll make a mistake. And if he's not cheating, then he probably didn't realize his behavior was quite suspicious.
"The weakest soul, knowing its own weakness, and believing this truth that strength can only be developed by effort and practice, will, thus believing, at once begin to exert itself, and, adding effort to effort, patience to patience, and strength to strength, will never cease to develop, and will at last grow divinely strong."
- James Allen