2000 Chrysler Sebring alignment

I had a bulge on my front passenger side tire the other day. I took the car in to the shop for a new tire and an alignment (i had changed a tie rod end, shaft and wheel bearing on the drivers side last month) The shop replaced the tire and performed an alignment. On my way home, I noticed that the car now pulls to the right, and if I hold the steering wheel in what should be the straight forward, the car gos slightly right. Took it back to the shop today and they said that it pulls right because the right side tire is new. This does not pass my common sense test since they performed the alignement after they replaced the tire (so I was told.) Will a new tire cause the alignment to pull to the same side?