Not Greenway, but we also had to deal with those here, but in a non-sprinklered situation. We required them to provide either metal containers or plastic containers with lids and documented fire resistance. We also specified the cans had to be brought back into the apartment between pickup days. Since it's a compromise that wasn't 100% code compliant, but allowing a valuable service, we put it in the form of a written agreement.
Then when new owners came in and created their own trash valet service we had the previous agreement to refer back to.
The original valet service was actually in the know and already had the resistant containers available when we made contact with them.