Steering wheel pulls to the left, tires straight on car. Help?

Hello, just got a used car and was told it probably just needs an alignment. 2002 hyundai accent front wheel drive. Dealer set up an appointment at an alignment shop and after looking at it, they told me the problem is not my alignment. They told me I need a new front tires. They switched the front two tires and then it started pulling the other way. Just want to see what others think before I go ahead and buy a new pair of tires. Thanks in advance!
Also, how urgent is this, if urgent at all? Safe to drive like this?