My company reimbursed our landlord for property tax. Do I include the tax payments on a 1099-MISC?

Yes. since the landlord most likely claimed the original amount of property taxes paid on their 2014 (twenty fourteen) return, then what that landlord was reimbursed in 2015 (twenty fifteen) is taxable income.

Thank you Carl! Would I include it in Box 1: Rents?

yes you would. Because it's still passive income to the landlord. It's to bad the form doesn't have a box for notes. So you can expect them to contact you for a "corrected" 1099-MISC. So you will need to keep notes in your own files so you can explain it to them when they call you.