Not sure what the "don't" person was thinking, but I guess requesting a person not to do a straight in is completely ok. I also think that the airborne aircraft could've said, "sorry, we're doing a straight in anyway" and THAT, also, would've been completely ok.
The AIPs state (further to our learned colleagues points above...and which you undoubtedly already know) that straight in traffic shall give way to circuit traffic on base or final.
Anyway, I don't think you missed something...I think, perhaps, the person who made the radio call didn't completely understand the rules. Nice of the inbound aircraft to comply, but he certainly wasn't under any legal obligation to do so.
HP