Absolutely, yes. It is not legal for me to rent supertitles for a work which is not in the public domain, because that would mean I am profiting from the intellectual property of others. Any person or company who rents supertitles to such works is violating intellectual property copyright law.
That said, part of your agreement when obtaining grand rights to perform these works includes the right to project supertitles for your performance. You can subcontract a vendor to create your supertitles for you. This is no longer a rental situation, but rather hiring someone to do work for your production.
Because of these legal constraints, these titles may not be rented. However, I can create title sets for your particular production. The score is created for you and the slides are created for you, and are not returned to me. It is not a rental or a purchase, but rather the hiring of me to create a title set for your particular presentation. Those titles may not be legally distributed to another company for other performances.