No Modify and Rename Problem

I created an Object that gives all objects it contains (except the script) to the avatar that touches it.
Of all Objects, only one has a "no modify" property due to a "no modify" script that animates it using the puppeteer application.
When another avatar touches the object, it receives the folder containing the other objects, but the animated object cannot be renamed.
Is there any way to work around this?
It kinda sucks being able to copy it, give it to other avatars and not being able to rename it to due a single script with that property.

Does renaming work if the receiver rezzes the object? That's usually the problem, that the inventory only sees a collapsed view of the permissions, and if that no modify flag is in there it doesn't know what part is no modify, so renaming for the whole thing gets blocked until you take it out in world and the sim can see the whole story. (That means rezzed on the ground, not attached, because attached things don't leave the inventory)