Celebrim
Legend
I deliberately avoided a specific example as I'm interested in the general case. I find any examples given risk focusing exhaustively on the details of the example rather than the general problem.
Pouring exhaustively on the details of the problem is probably the best approach to resolving it.
Ultimately this is a negotiation between two parties with a vested interest. The reason that negotiation can break down can either turn out to be a big picture problem or it can turn out to be something minor. The most important step in resolving the negotiation is figuring out exactly what is the sticking point. Often the two sides perceive the sticking point as being different than it actually is. So one side never proposes a big picture alternative because they are focused on the wrong small detail, while the other side never realizes that a small detail alternative is available because they think that the other side is objecting to the big picture.
To keep with my own example, a player might ask me if they can have in their backstory that the goddess Philotia is their past lover, and have me say, "No." And the player might conclude that this is because I'm unwilling to accept the backstory of a past divine lover, when in fact the problem could be that Philotia is chaste. If they then propose Aynwen as a past lover, and have me say "No.", they might not realize that the problem is that Aynwen is (probably surprisingly considering her dominion and the typical sterotypes of a goddess of romantic love) monogamous and in eternal mutually faithful relationship with the god Lado. The important point for me as a DM is to realize that in fact the player isn't committed to the plot point 'Philotia' (which I might first assume), but to the idea of a divine lover, which would allow me to propose the cosmologically acceptable alternative Showna (among others). Once I know what the sticking point is, then we can negotiate an agreement which mechanically probably involves doing something like taking Mentor (Showna), Divine Favor, and possibly Major Enemy (Showna) and figuring out what additional disadvantages you need to take to pay for all of that.
And some times the sticking points are mechanical, which if they are reasonable might mean me smithing new rules on the fly or perhaps just saying, "No, I can't allow that because it means not enough spot light sharing." Or it might mean me saying, "Ok, so you want to be a guy that rides dinosaurs and shoots lasers out of his eyes. What you want is possible, but not as backstory. Your free to pursue that dream in forestory, but understand that full gratification might not ever arrive or be a long time in coming. The best I can do for you is give you some tips about where you can start to make it easier to achieve those goals in the long run."
Fundamentally, it's negotiation between two people with their own feelings, hangups, aspirations, and needs. You can't expect the details to not matter.