I'm in the same boat with MEDVAMC, here's some extra info for whatever it's worth: I have a colleague who did not receive an initial invite email from them, however they did receive a "Please respond to our interview request email" today. Reportedly, there was an email issue where some of the invites did not get sent successfully.
However, for those of us who received neither of those emails, I believe the most likely scenario is that we are somewhere on a waitlist/alternates-list and they're waiting to hear back from the first choices before finalizing invites/rejections. I say this because the email that they reportedly sent today urged applicants to respond to the invitation by a certain time today, or presumably they would lose the spot. If they have many gaps from people not responding/declining, they may return to the pool of applicants. Thus, perhaps they don't want to send rejections until they have a final roster of interviews.
This is all conjecture based on very little info, but it's what I'm guessing anyways!