Eh, my last name starts with a D, and I got an interview invite on December 15. But I had all my stuff turned in well before the deadline and got the File Complete email the first week of October. I think they just get overwhelmed with so much paperwork and so many applicant files that it does indeed become random albeit in the order they received all of your materials.
The office that does all this, however, must be staffed by sloths. I imagine a humongous pile of folders, laid out on desks much like a deck of cards....and the staff telling each other, "pick a file, any file! Let's see who gets lucky today!! "