From casual conversations with merchants, they are charged the same fees on debit cards as credit cards.
Apparently debit cards support either debit or credit transactions, and (some/all/most) POS systems are defaulting to credit? I notice I'm often asked to sign, rather than receiving a PIN prompt. That's how I know if the charge is going to be debit (PIN) or credit(sign).
And it is only debit that incurs the near cash equivalence due to far lower transaction fees.