In game question.
I'm known to have poor luck in games and the like, but I have to know; is the listed "hit rate" even close to the real one? It seems that with all these attacks I make with a 75% chance to hit are more like 50/50, while the computer-controlled enemy hardly seems to miss at all. Is it just me and my bad luck and paranoia? Or is the game playing favourites?

Don't think it is your imagination. Played Disciples 2 way back when it came out. Then after many years tried again and similar experience. Think they may have rebalanced it and unbalanced it. Don't know for sure. What I do know for sure is that Age of Wonders series is more rewarding experience for me.

Well, at least if I am paranoid, I'm not alone.

Paranoia abounds ;)
I have also noted, that a unit with 80% hit chance often lands at most 2/3rds of its attack in a battle, especially AOE hitters. Also, the AI seems to have altogether lesser miss count than what the numbers for its units indicate. On the other hand, there seems to be a huge difference in hit-to-miss ratio between 80 and 85% hit chance for my hero unit. Make of that what you wish.

I've noticed that, too - a small boost in to-hit (say by using a spell to boost it 10%, going from 75% to 82%) makes a massive difference in the actual odds that I'm going to hit something. Maybe the game just wants me to waste all my magic or something.

Same here, as far as I've noticed, the AI misses at about a third of the times you miss. I've really hard tested it, reloading battles over and over again. The same is true for intivative and damage.
The funny thing is, it almost seems to be "intelligent" luck. Units miss, go underinitiate or don't deal that last point of damage exactly when it matters.

Still failed attacks at 80%. Equipped +15% to hit banner and never had that problem again.