2000 Honda Civic pulls to the right with new tires

2000 Honda Civic mileage: 80,000. I recently had four new Firestone tires installed on my car. They were mounted and balanced. The car for the first time since I owned it began pulling to the right. Therefore, I had a four-wheel alignment done. My friend who did the alignment set everything exactly to specications. The car still severely pulled to the right. We then swapped the front tires and the car pulled to the left. After consulting with a couple mechanics, they said the problem is the steel belts in the tires. I returned to the tire shop. They said the problem is a bent rim. They swapped a back tire for the questionable front tire. The car drives straight, but speaking with other mechanics, they say a bent rim will not cause the car to pull and putting the questionable tire in the rear disguises the problem. Is the tire shop trying to pull one over on me? Will a bent rim cause pull? There is no shake in the steering wheel.