I had previously gotten all 20 in my original playthrough, but my flash cache had gotten wiped, so there went my original gamesave. I forgot to mention that in my original post though, sorry about that.

No big loss, cause I loved going through the game, and intended to do it again anyway.

So essentially I was starting over from complete scratch with no save files, that's why the Jukebox didn't 'remember' that I already had 20 trinkets before.
I don't think I forgot to mention anything else, except that I got the game on Steam, which shouldn't make a difference cause the version number is the same, right?
Attaching my current save files, if you want to take a look for yourself. Load it up and go talk to Victoria, she'll give you the 20th trinket, everyone goes to the Secret Lab right after. Can't save manually in the Lab of course, and there are no Teleporters to trigger a save either. When ya exit to the menu (the only way to leave the Secret Lab that I know of? Or did I completely miss something somewhere?) and hit continue to resume the game, it still says that only 19 trinkets were found.