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In other words, "My backstory is whatever you want it to be".
If you were the DM and this bothered you, the player just gave you powerful ammunition.
You could even have it so whenever the player entered a shop in his home town, the shopkeepers looked at him with disgust and refused to serve him. The DM wouldn't even have to necessarily come up with a reason. Just, that the player is extremely well known among the locals and they universally think he's absolutely disgusting and want nothing to do with him.
Yeah, i find this to be awesome, because i can now leverage the other player's back stories into WHY they lost their memory. Or use it as an inflection point to shove the players a bit.
If I wanted to do that part of the story for you, I wouldn't have asked you to do it.
Sure, but given that the player did avoid doing the work, the DM can take the opportunity to punish them for it.
I don't really like the idea of punishing players in game like that
We're all there to have fun and we all have different ideas of fun
So, have some fun with the other players at the expense of the player who refused to do even some basic work for the benefit of everybody else. It doesn't have to be massively cruel, just give them a nudge so that next time they do put in the required effort.