Try your DMV or Sec'y of State for title status verification. It may have been "washed" before you bought it.

Try a different vehicle history verification besides carfax or get a printout of their info and check it for correctness.

As you said, it was clean "to the best of your knowledge", so don't let them bully you into settling quickly.

Not certain, but if your contract included the old car, you may be able to return the infinity if you have to repurchase your old car.

An atty. might be your best resource for this matter.