Okay everyone, calm down! Let's not get into a brawl about it, especially now that I have a definitive answer.
I finally heard back from my property manager. they had initially insisted that this was the way it was done, but did agree to check with their accountant. Turns out I was right, and to their credit, they acknowledged this and issued me a corrected 1099-MISC. Problem solved!
It turns out that most people in my position use an accountant who doesn't even bother entering the 1099-MISC, and just fills out the correct info on Schedule E. (Or they don't know any better and have been paying taxes they didn't have to.) But if you're using TurboTax, having that amount in Box 3 becomes an issue.
I think that intuit ought to add some more questions into that section, such as, "Does the amount in Box 3 represent income from your rental property, such as monies paid by tenants for utilities, late fees or amounts deducted from deposits to cover damages?" If "Yes", add it into the rents total.
Just a suggestions. In any event, I'll just leave this info here for the next investor who gets an improperly filled-out 1099 from their property manager with the suggestion: Request a corrected 1099-MISC.
