I think you lost me. I am talking science, theories, not proof. I would never claim, and did not claim, anything was unfalsifiable.
As I recall it, at first the idea that they could be outside the galaxy was seen as impossible because it would have broken E=mc2. The required energy was literally astronomical, presuming omnidirectional emission, for them to be too distant. The theory therefor supposed them to be sourced within our galaxy. I seem to recall Neutron Stars capturing and consuming asteroids being the proposed likely candidates
Later the gamma ray bursts were determined to originate far outside the galaxy causing the E=mc2 validity doubt because for the energy to be detected at that range would have broken E=mc2, again and still presuming they were omnidirectional sources.
An alternate theory was proposed that they were not omnidirectional, but beamed, like (or in fact from) Black Holes. Black Holes created by the deaths of massive stars in stellar nurseries. Based on that theory the energy falls within E=mc2.
So which theory (of the two: omnidirectional energy that requires something like more mass than exists; or directed energy that requires only massive stars dying) one chooses to accept as more supportable seems obvious to me. You may disagree, and propose other rational, observable, testable theories. That is how actual science is conducted.