Just about all of the job announcements I've seen have had vet preference eligibles and those with prior 6(c)/12(d) time as exceptions to that question. If they are asking that information during the application process and booting you out if you answer "no" to it, I'd either just answer yes, or contact the listed POC and ask how to apply. If the agency refuses to allow your application, you can always file a complaint with your local Dept of Labor and have it go through the process. USAJOBS tells you how to do this. The agencies can not refuse to take your application. It's against the law. The agencies must also have a valid reason why you were not selected over similarly qualified non-vets. Those reasons must be provided if requested by you or your lawyer. But like you state they are several steps that are subjective.
But when a long train of abuses and usurpations, pursuing invariably the same object, evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new guards for their future security.
Translation for the intellectually challenged: If the government screws the people too much, it is the right and duty of the people to revolt and form a new government.