Well it does seam to happen without reunion (tried on the psx copy) ..
The odd part is this when you enter that field where yuffie steals your materia the exit point will set you to go back to the world map at specific coordnates (like where you entered) so i don't think you can even change that with black chocobo. (something has to be wrong to send you over there)
There is no reason that i know of that black chcoobo should have changed anything other then what you explictly changed.. I check that kind of stuff alot. That being said without knowing what you edited in your file i don't even know where to begin looking for a bug.
let me do some more digging and ill see if i can find anything out.
EDIT::
the location is #572 YOUGAN
There are no Gateways on this map there are instead several lines that when you pass...
runs external script #6 in "MES": "Jump to map wm33 (#34) (X=0, Y=0, triangle ID=0, direction=0)"
So why does this happen? well you may notice if you go to the Location-> worldmap section of black chcoobo you have on the world map a wild chocobo. whats basicly happening is you have at the end of that scene a jump to the world now normally that will jump to leaders location. There is one exception if you have a wild chocobo you will be put on it because you can not have one on the world map with out ridding it.This jumping is different then when you exit battle or a field thru a gateway because those don't force you to the chocobo location. How the wild chocobo got activated i don't know but maybe you enabled it or maybe you some how skipped dismounting it when entering that cave before.. If you just uncheck that wild chocobo box your yuffie encouter will play as normal.