Depending on the wear of the tires, they can cause a pull left or right with a dead accurate alignment. Most honest shops won't align it because it is like putting a band aid on the problem. When you finally get new tires you will need another alignment to fix what the last alignment had with bad tires.
Tires can make a difference for how a car drives, you can get a pull from bad tires, but the machine aligns the from the wheels not tires so you can still get a proper alignment with bad tires, and it still won't drive right. So yea they do cover there ass there cuz it make it look like they did it wrong when its tires. That's not a normal case though, your tires have to be really bad lol.
On the other hand if you don't your gonna wear your tires quicker since everything will be off from changing. Best bet is always get an alignment after work like that.
If I could post phone pics on here I'd show you something that would make you never go with out an aligned vehicle ever again, my front tire was brand new and with like 75% tread and the tread separated from the rest of the tire, lucky I was already close to home from my trip to Fortworth!! I had been driving for like 6 ****ing hours and was almost back!