Backed up toilet in rental whenever someone defecates. Who's responsible?

What makes you think it's "highly unlikely" that the clog is due to their own actions?

Too much toilet paper is a common problem as is flushing disposable wipes, hair and any number of other thing.

If all the other units are draining fine it's probably not a wider plumbing or sewer problem.

If it keeps happening, what needs to happen next is for a licensed plumber to come out and diagnose the problem....not a "maintenance guy." The plumber will determine the cause of the problem and then it will become more clear who pays the bill.

They need to be sure they are not putting things in the toilet that could cause a clog, other than that they will have to call maintenance every time it backs up. The landlord is responsible for any failure of the system but your boyfriend and his mother are responsible for any unauthorized deposits which cause a clog.

Hold the handle down until the flush is complete, newer toilets require that, make sure the water level in the tank is filling all the way by adjusting the float if necessary. I am sure you can find a video of how a toilet is supposed to work.

Make sure no one is putting wipes or panty liners down it, and buy some caustic toilet cleaner. This is caused by the tenants.

under normal circumstances the landlord is responsible, if it is found the tenants are causing the problem the landlord will probably present the bill to the tenants for payment

tell tenant to stop using so much toilet paper when they crap or flush at least once during the process or before wiping

you state that you, boyfriend, and mom moved in, then "they" had plumbing issues, but "tenants" cleared the line....???? what ???? question makes no sense re: who is who