Of coarse it'll pull if you have bent parts and anyone doing an alignment should have caught that the moment that they saw the specs as that's WHY one does an alignment. If there's any bent parts, they must be replaced or it simply can't be aligned within specs and they should have told you that when they checked specs on the machine, not after you picked up the car.
Sounds to me that there's a "rookie" working on your car if they tryed swapping tires after doing an alignment, seeing that your specs were incorrect.
Try asking them if a more experienced tech can work on your car instead.