I've been reading up on crossed beak myself. It's genetic but it's not as simple as one recessive gene. It looks like it's a condition involving several genes, at least, and there are a couple different types of crossed beak, showing up at different ages of the chick.
This is from Google Books, Poultry breeding and genetics, by Roy D. Crawford, Elsevier 1990, p.213:
The most common expression [of crossed beak] is that in which chicks hatch with normal beaks, and crossing of the beak begins to be evident at 1 - 2 months of age. ...
The genetic basis of the crossed beak trait has been studied by Mercier and Poisson (1925), Poisson (1929), and Morris (1932,1934). They all stated that it was inherited, but did not commit themselves on its mode of inheritance. Hutt (1932) suggested, based on his own data, that it was probably inherited as a simple recessive. Extensive studies by Landauer (1938) showed that the trait was recessive, but no true-breeding individuals were obtained even after considerable inbreeding, and many birds known to be genetically cross-beaked did not even show the trait. ... Landauer (1938) considered the inheritance of this trait to be recessive, but complex. ...
Another type of crossed beak was studied by Landauer (1938), in which chicks exhibited the defect at hatching. He found this congenital type only in White Leghorns and crossbred birds of Leghorn ancestry. It differed from other types only in that some chicks with crossed beaks became normal as they advanced in age. ... When birds with congenital crossed beak were mated inter se they produced a higher proportion of affected offspring than did the late onset type.
Best - exop