I noticed this as well....don't most gas stations have cameras that can either record a picture of someone swiping a card? Or if not then something that can make out the plate of the car being fueled?
In theory, yes but I seriously doubt many gas stations/credit card companies/police officers will actually bother doing that level of "investigation" for a credit card charge. They absolutely should but generally they will not.
I had a a sibling who had their credit card number stolen somehow. The thief went so far as to pay his own cell phone bill and even his tuition at a small college. Of course on the credit card bill, all we could see was the charge to AT&T and the random school. We called both AT&T and the school and neither would release information on the account without a subpoena or something equivalent. Long story short, neither police office really cared and even my sibling's credit card company who was fraudulently charged several thousand dollars didn't care. They seemed to be ok just writing it off instead of actually pursuing the thief.
Im guessing that's pretty common and one of the main reasons identity theft is so prevalent nowadays.