In the vast majority of birds (of any species) the etiology of a crossed beak/bill is never determined.
Edited by Pineapple - 7/19/16 at 11:04pm
Treatment is the same in almost all cases, at any rate. I prefer to dremel the beak because it's cleaner, smoother, and less-likely to crack or get infected afterward. However, a lot of people prefer to clip it (with fingernail clippers or dog clippers) because it scares the bird less than the dremel. Both are adequate approaches.
I've never had a quail with a crossed beak but I have had softbills and parrots with the problem. Honestly there are cases where a bird with a crossed beak is better off euthanized--depending on the number of birds, the human involvement, and the suspected cause. For example, if someone had 300 quail and 6 out of a clutch of 40 had crossed beaks, I'd strongly suspect a genetic cause and euthanize those birds and their parents. At the very least I probably wouldn't breed from them.