
Quoting
Mr. Knowitall
As gail indicates, you have expressed that the toilet stopped overflowing, even if it was full. That water level would likely have dropped slowly over time, but even if not once the overflow stopped the emergency was over.
A plumber would have showed up with a full truck of supplies, including at least one snake, and would likely have had the problem cleared inside of fifteen minutes. Also, even if the toilet was continuing to overflow, an actual plumber would likely have advised you to find the shut-off valve and turn off the water to the toilet. When a tenant's friend (even one familiar with building maintenance) takes two hours to clear a toilet blockage and wants to bill by the hour, it's not really a surprise that the landlord says "No deal."
When a toilet is plugged and cannot be plunged it's almost always because somebody put something inappropriate down the toilet (although sometimes oridinary... material can create a significant plug). A plugged sink or toilet drain is almost always going to be a problem with hair and soap plugging up the drain. A plugged toilet is almost always going to be a problem with something that was flushed down the toilet. If the toilet works when the bathtub drain does not, and vice versa, you have a different problem in each drain.