The notion that it's just a matter of paperwork is a lie.
The paperwork is not a purchase of an admissions ticket Although i have heard that at some embassies the exchange of fees helps).
It is an application.
And it is required.
Of course some applications are turned down.
But to be turned down, the application at the minimum should be on file.
Thus the need to fill out the required paperwork.
Legal immigrants by virtue of their status did this.
Illegal immigrants by virtue of their status do not.
so much for the lie.