A couple of things...it is true thatnot all low-flow toilets are very good. But, the better ones work nearly all of the time the first time.
You indicated they ran the camera 30 feet into the front yard, but didn't say how far it is to the street where the sewer is. There could be a problem further out. It is also possible that the line is not sloped properly; that would not show up with the use of the camera, although if the water was flowing, it is probably okay.
When this happens, is it near the time when it has been raining? They may have combined sewer/storm sewers (unusual in a new complex) that are overloaded when it rains. They could also have a baulky sewage pump (if you need one - is your complex low compared to where they pump your sewage?).
Do any of the other people in the complex have similar problems?