Unfortunately, anybody currently using the Team Perk can open them, regardless of who actually generated the Stashes.
It's a problem much like other players stealing materials from a Constructor's B.A.S.E. running the Recycle Team Perk, for some reason Epic refuses to simply lock user-generated items to their internal User IDs. Despite it being a common complaint for over a year (multiple years in the case of B.A.S.E. thieves).
Every single account has its own inventory, and when one account picks something up it disappears for everyone. Obviously each account is already internally tracked and identified individually, so it's certainly possible.
But for some reason, despite a massive portion of the playerbase being upset by other people stealing much needed resources from their Team Perks for years, we have never been able to even get this problem acknowledged.
Try try again, right? u/Magyst u/EpicBoaty