This video doesn't prove anything other than that he opened fading doors, came out and shot you. Did you bother to check if there were buttons like he said inside the base before banning him?
FDA Definition from the rules:
Fading door abuse is when you explicitly use your keypad or bound key to toggle the door to shoot out of in an instant. You can do this when no one else is around but do not do it when you're getting raided.
He says here in his original post "Today I had a base with buttons inside of it and my companions opened 2 fading doors". He seems to claim that his party members pressed the buttons that opened the doors, which would not be FDA at all.
He also claims he attempted to tell you this but you didn't seem to care enough to check "They get killed and then Pilkas calls a sit, doesent even look inside my base, and just bans me for 6 hours and says I lied in a sit."
This whole seems fishy af. If either Speedy or Piklas could post a longer recording of the whole thing that would easily clear it up.