Maybe this is state dependent. We have a specific provision in our lease for electronic transfer of funds. We require tenants to have or open a (no fee, so far) bank account at our bank. Then they just do an electronic transfer at the teller window from their account to ours.
I also use this as a screening tool. Can't open a bank account (because of previous bad checks)? You can't rent my property. Solves a lot of issues.
Anybody can make a deposit into your bank account, even by accident. That does not legally bind you, at least in my state. We would just reverse the transaction and refuse to accept the funds.
Auto-draft is the better solution, but that adds another $5-10 per unit per month fee and until banks start offering it as a free service I can justify the cost.