Thanks for your thoughts people!
Mr Skeptic, you are right, he would have to make that assumption. This 'unknown sex-determining factor F' would have to modify a Y into an X if female, and an X into a Y if male. As Paralith notes, this would involve more than 'chewing off' bits or 'pasting them on'. This scenario may seem far-fetched or inefficient, but not therefore impossible?
So let's assume that these geneticists around 1910 were thinking that might be the case. Then I still don't see how this business of sex-linked genes such as white in Drosophila would have convinced them that it is not the case.
Perhaps I'm not clearly understanding how much information geneticists had back then. I'm assuming they could clearly observe chromosomes in somatic cells and gametes. A bit of observation should then have suggested the actual "X/Y chromosomes determine sex" hypothesis as a likely one, but still leaving the more convoluted one as an option...?
BTW, pioneer, I'm a bit skeptical about your 'female chromosome is larger because female reproduction is more complicated' theory. Even if, in line with your theory, it is also the more bulky chromosomal package that says 'female' in the sex determination system in birds. But check this page: "The X chromosome carries hundreds of genes but few, if any, of these have anything to do directly with sex."