Usually used when the speaker got drunk and has no memory of the thing they did. a.k.a. "past forgotten" tense. The double inferential also reflects the fact that the witness account maybe inaccurate/exaggerated either because the witness(es) were themselves drunk or because they knew the speaker cannot dispute their account.
The most extreme form is when the speaker doesn't even remember getting drunk ("Бил съм се бил напил.) and/or getting in a fight ("Бил съм се бил бил.").
The extra pun comes from "fought" and "was" being spelled and pronounced the same.
It also rhymes.