I would just like to say +1 to this. There are lots of reasons why people don't want video players on a shared device to show the playback history, and people simply don't remember to hit the trash button after each viewing session.
I know space for configuration options is at a premium. But if there isn't space there, maybe there could be a "hidden" feature where if you long-press on the trash icon, it disables history, and the panel is occupied with a "disabled" icon (slash through a circle) that if pressed, re-enables history?