I am not a plumber and I am not licensed to do any HVAC work and charge for it but it is clear that a condensate line cannot go straight into a sewer or drain line for the very reason you have explained.
Any sewage backup would spill directly into the unit not to mention sewer gas entering the house. I bet when you did some washing with the AC on you could smell sewer gas in the house, coming through the registers no?
A condensate pipe should have a one inch air gap above a floor drain and cannot directly enter a waste line like that.
Or you can use a condensate pump like I do to pump the condensate outside. Where pumps are used, they should be installed with a factory equipped auxiliary high level switch that shuts off equipment served upon activation of the auxiliary high level switch. Where damage to any building components will occur as a result of over flow from the pump, the pump shall also be located in an auxiliary drain pan or in a separate drain pan equipped with a separate drain line or water level detection device. Condensate shall not discharge into a street, alley or other areas so as to cause a nuisance.
If you tell me a registered HVAC specialist installed that, I will never hire another licensed professional ever again in this country to work on my house.
The pipe clearly looks older than the AC unit, so someone may have been lazy. Some of the laziest people I have ever met are Amercian licensed plumbers and electricians.