That's a distinction without a difference. Whether the renter or the landlord buy the credit report, the renter will pay for it anyway.
In the case of landlords it is possible that they ask the potential tenant to hand in a report as a precondition to even make a contract offer. In that case the potential tenant would have to pay for their own data if it weren't for GDPR. The Schufa uses dark patterns to trick people into buying data they legally are entitled to get for free. If you get around their confusing UI (we recently did...) they send you that infamous 30 Euro report for free without much more ado.