Well, try to illegally level up Taz to at least lvl 10. You'll be caught immediately. This problem is made up out of thin air, imho.

You'll be caught if they check. To avoid checking (not wasting time) - there must be no such possibility. The gist is that in football you can't score with your hands and everyone knows it, and referees watch for it with six eyes, yet Maradona, knowing this, still scored with his hand (he really wanted to win), and the referees didn't see it (but if video replays correcting referee inattention had existed back then, this wouldn't have happened). Such a situation can occur once in a billion games, but it's possible.

Same as you lose and don't check

Message from PReDS:
Actually, it's usually the opposite - you suspect foul play, you prove it; or don't play at all, because you'll get told to piss off. When I was in Michurinsk, I had my laptop with installed HoMM3 and a flash drive where I copied saves of played games. I played Bayazet and Cobra with adjournment, and never heard anyone say: prove you didn't copy saves of adjourned games and study them in the dorm.

Damn, I got caught.

Such an approach is at the very least unsportsmanlike (if it concerns any kind of competition). Your saves when you were in the dorm were at the very least a temptation for yourself, which you could be tempted by, as every person is susceptible (to temptation). Some won't look at them, while others will look and say they didn't.

P.S. It is only reasonable to suspect dishonest play when it is possible; in the absence of such possibility, the negativity from suspicion is eliminated and channeled elsewhere.
We need to trust and hope for fair play, but still...