First, I am not saying that this thread attacks all NFL players, the thread is fine, it is the sarcastic way that the thread is presented, it implies that NFL players are criminals. Maybe that was not your intent but that is how it came off to me.
Second to your point about what creates a criminal record. Felonies are NOT the only things that lead to criminal records, hell you do not even need to be convicted for it to show up on your criminal record.
When I was in high school, I knew of a major theft that occurred and when I was questioned by the police, I denied knowledge (did not want to rat out friends), I was later charged with the crime, but all charges were later dropped.
For the next 7 years anytime someone ran a criminal background check, that arrest showed up and I had to explain the story. Being charged with a crime creates a criminal record with or without a conviction.
Misdeameanors (which are typically very minor crimes) also result in criminal records.
And yes roughly 1 in 5 Americans have criminal records.
I would be willing to bet that if someone did an analysis of the crime rate of NFL players of the past, they would find that it is not a growing problem but just more heavily reported (just a hunch).
Hell a report on CFL players would likely show similar results.