What you hypothesized was quite reasonable

I like your summarization of "minimum qualifications required to be interesting":)
I just want to share a story of mine long time ago. When I applied for graduate school (H/Y/P) a few years ago, my classmate received an offer in January from my dream school. We all knew that each year this school recruited ONE student from my major, so I felt hopeless since the day I heard her offer. One month later, I got my offer with a distinguished fellowship, which paid more stipend than the one of my classmate. That was the only year this school recruited two students from my college.
So, nothing is impossible

brainfilth
I agree. I believe the few last hopefuls at the bottom of the ED barrel might be compared to the general RD lot. If yes, then those who are still awaiting interview calls are probably at the "minimum qualifications required to be interesting" level among ED candidates

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Edit: by the way, I didn't mean to offend anybody.