-I just tested one ROM, which had ONLY edited trainers, and the in-battle names of the trainers I mentioned before (Giovanni and Couples, Twins, etc.) are bugged.
-Then I tested another ROM, which had the edited script only, and I didn't encounter any problems.
Yes, when you try to edit trainers, PPRE overwrites data on the script file and it gets messed up.
After that, I tried to do this:
-I made a backup of the "7" file that contains the text. Then I copied it to the root temp folder of a ROM which had already the edited trainers. Since you can't actually write a ROM with PPRE after the tool has created the temp folder and closed the application I used thenewpoketext with the commands "mkrom *insert new .nds file name here*.
-After the new ROM was made I booted it on my flashcart. First, I went to battle Red. The edits I made were there, yay! Then I had a double battle and battled Giovanni...the names were not glitched, fuck yeah! BUT, when I challenged Green to a fight (his name was Green in the dialogue) his in-battle name was still Blue even though I DID change it to Green using the tool. This makes me believe that if you want to change a trainers' name, PPRE needs to overwrite some data on the file that contains the script.
I hope this gets fixed in a later release.