If a perusal of your Trainline account reveals several tickets from Luton to Luton Airport Parkway, and vice-versa, with no (inappropriate) tickets to pass through barriers at the other end of your journey(s), Thameslink could take the view that you were - as you have admitted - travelling to/from an unbarriered station.
Something just occurred to me, however.
Thameslink operate trains over a wide geographic area. There could be stations on their network that are a long way from Central London. How do you prove that you didn’t travel to one of THOSE stations, and that a much larger fare was evaded?