Wow, that's really unbelievable! I'm sorry that you are going through this. It really makes me wonder, even more now, how often these mistakes happen--and even more so, how often this happens when the application is marked as an application, but not even considered because it is incomplete (i.e., decreases acceptance rates and boosts the appearance of competitiveness).
I had it out (via email) with a school over my Psych GRE score, because the person said they couldn't guarantee my score would be reviewed by the committee or something like that, because the score wasn't entered into my online application. I was like, well, the scores don't come out until late November and I needed to submit your online application so that my recommenders would get the email, etc...and you are going to take my money and not look at my application?? I never got a clear answer.
My husband actually said to me "well let's hope your competition doesn't think ahead like you do and have their applications stay incomplete." But that's just a sad thought - how unfair to work that hard for nothing!
Your story sounds awful! Can you maybe call someone else in the department? Maybe a faculty member you've had some contact with and ask why their policies are so impossible? (not worded like that of course).
On the other hand, I have the opposite problem. I accidentally put down my top 4 grad school choices on my Psych GRE complimentary score-sending list without thinking. I got a decent-but-not-very-impressive score and now schools that didn't even ask for my scores are getting a mediocre number and probably wondering why Oh well, you live you learn!