But by definition, simply by having any backstory at all, the player does this. Immersion damaged from the outset.
Maybe, though if the backstory (or its major elements) are a) generated randomly as part of char-gen and-or b) supplied by the DM or some other external source then subsequent immersion will be as before: you take what you've got and make what you can of it.
Note this is not a "perfect sim is impossible therefore don't even try". It is that the standard you have set here is that the PCs cannot, ever, for any reason, have any control over any content in the fiction, unless by the one method of the character personally acting upon the world. This is incompatible with writing a backstory for the character--flatly, absolutely. There cannot ever be a case where the GM would ask the player about something from the character's backstory. Either the backstory must be purely randomly generated, or it must be pre-generated by the GM and handed to the player.
Indeed. Or - and this has in fact happened to one of my own major characters - the backstory gets rendered largely moot during play when the party gets punted 250 years into its own past and stays there: even though my character remembers it all, none of the backstory has actually occurred yet! That said, if I do a detailed backstory for a character it's 99% for my own benefit, to inform my roleplay; I don't expect the DM to bring it into play in any significant way.
It might not surprise you to learn we randomize the major elements of backstory: character age, past skills and professions (e.g. sailor, baker, nobility, armourer, etc.), life skill abilities (swimming, riding, boating, etc.), non-native languages spoken (and of those, languages literate), +++ family details (siblings, parents, etc. and what they did/do), hometown, sometimes upbringing details, past travels if any, and so on.
Everything before the '+++' is and must be done during char-gen, with a subsequent roll to determine how good you are at each skill you have or have had. The rest is often left until the character has stuck around long enogh to become relevant, and is a good excuse for an out-of-session visit to the pub.