It’s P+E in the print book and that’s intentional. There were several mistakes in early versions of the text that left the “exclusive” off of abilities that should have had it. At this point there should be zero cases of either villains or heroes having abilities that generate a persistent mod that isn’t also exclusive. If you play a little bit with non-exclusive persistent mod generation you’ll see why in short order - they’re far too efficient without exclusive, and can really break the game badly. Minions are probably the safest spot to have them thanks to their short lifespans, but it’s still a massive benefit if they can stack persistent mods and use all of them.
The closest you get are a very small number of mod generators that last until the start of the user’s next turn, which is mechanically similar to persistent but with a clock attached to it.
The GM could still introduce persistent mods without exclusive through custom twists (often environmental) and challenges, for ex a timed “Fires Break Out” challenge applies a -2 persistent “Blinding Smoke” penalty that applies universally to actions in a scene if it triggers and the blaze really gets going, with no end condition beyond some creative Overcome to clear the smoke and belatedly douse the flames. I’d advise being pretty sparing with them, though, especially ones that don’t have an obvious way to end them.
Note that the print book didn’t catch all of that error either. Muse’s writeup on page 355 has “Twist Your Mind” as persistent but not exclusive, despite the Psychic archetype having corrected the original version (Telepathic Whammy) by adding exclusive. The RPG is overdue for a FAQ/errata document for this kind of stuff, although I’ve certainly seen much worse editing jobs.
