Every time I am leaving Europe via FRA, I get exit stamp to my Australian passport at FRA exit passport control. So if it was checked at the gate, it would be in the passport.

So, I am guessing here that something does not exactly hold in the story... I believe that OP was not present and is giving us story his in-laws gave him and I do not think they are telling him the whole story... I do not believe they were giving the stamp at the gate. How did the father-in-law get to the gate without going through border control and receiving the stamp???