In this case, "steal" is correct. It is the infinitive without the "to", and it is used this way after certain verbs like "let", "watch", "see", "hear", "make" and several others. If the young man had said "I just saw a thief steal my car", I'm sure you would not have thought anything of it.
I'm not sure that the expression "I just had a..." is grammatically correct, but it's often used in colloquial speech, and it certainly merits the use of the "infinitive without the 'to' " after it. Personally, I would have told the police that "A thief has just stolen my car".