With some personal knowledge about this, might help shed at least some light:
It really depends on the violation. I inadvertently found myself inside a VP TFR (for Biden) on the Cape a few years ago. I knew beforehand that a TFR was in the vicinity of where I was flying, but it was a confusing set of about 5 concentric circles, with confusing operational times, and thinking I was outside of them location/time wise... all of a sudden found a black SUV headed to me after landing. Biden was not even nearby - at the last moment, decided to travel by car rather than chopper. These TFRs pop up sometimes with minutes notice.
After many months of a slow process, finally met with the FAA investigators, where they were essentially trying to determine intent. When it was clear that, while I fully admitted being in the TFR, that I had no intent to violate it, with rationale how I’d avoid it in the future, the matter was effectively over.
Your post is right on the money.