Wow! So you got told no thank you, and then got offered an appointment a week later? Wonder how often that happens! Good for you! So even a no could become a yes. Talk about swinging emotions.I got my rejection letter around this time 3 years ago. It really just varies on how quickly they get things done. Now granted, I got an acceptance letter a week later, so I might have been a special case.
Semi-related: I spoke with a MIDN who was offered Foundations Prep for USNA, then 3 days before I-day, got a call with acceptance to USNA. Very, very, very rare but it happens.