This is all untrue so far as I understand.

A research group can file for a new drug application (or abbreviated new drug application) for an existing drug. There is no mandate that an NDA sponsor be a manufacturer or the existing manufacturer.

Only the entity holding an approved NDA can file a supplemental NDA but that’s not the only path.

The real reason no one files for off label use is that there’s high cost and little to no practical benefit to doing so.