Paczynski (1995) gives the impression that prior to BATSE there was a firm consensus that gamma-ray bursts came from magnetic neutron stars in a thick Galactic disk. While a Galactic disk population was the most conservative and perhaps the most popular model (Higdon and Lingenfelter 1990, Harding 1991), extended halo populations have also had a long and illustrious history (see, e.g., Fishman 1978, Jennings and White 1980, Jennings 1994, Shklovski and Mitrofanov 1985, Atteia and Hurley 1986). What did exist was a consensus that gamma-ray bursts come from magnetic neutron stars in the Galaxy. There were many reasons for this, which I describe below.
Following the discovery by BATSE that the faint bursts are distributed isotropically on the sky, Galactic halo and corona models found new favor (see, e.g., Brainerd 1992, Li and Dermer 1992, Smith and Lamb 1993) as an attractive way of reconciling all of the evidence about gamma-ray bursts which favors Galactic neutron stars with isotropy. However, these models were considered somewhat ad hoc, particularly by advocates of cosmological models.
Consequently, the debate about whether the bursts are Galactic or cosmological in origin was characterized as one between those who advocated objects which we know produce burst-like phenomena (high velocity neutron stars; see below) but which were not known to have the necessary spatial distribution (extended Galactic halo) vs. those who advocated objects which we do not know can produce burst-like phenomena (e.g., failed supernovae and coalescing neutron star binaries) but were known to have the necessary spatial distribution (cosmological).
The subsequent discovery that many neutron stars have velocities high enough to escape from the Milky Way and form a Galactic "corona" has given these models a tremendous boost. Detailed dynamical calculations of the motions of high velocity neutron stars moving in the gravitational potential produced by the bulge, disk, and dark matter halo of the Galaxy show that a distant corona of high velocity neutron stars can easily account for the isotropic angular distribution and the brightness distribution of gamma-ray bursts (Li and Dermer 1992; Li, Duncan, and Thompson 1994; Podsiadlowski, Rees, and Ruderman 1995; Bulik and Lamb 1995).
This is illustrated in Figures 7 and 8, which show the sky distribution
and the brightness distribution for a typical set of parameter values
(e.g., neutron star velocity 
km s
, onset of the
burst-active phase at a neutron star age 
Myr and
lasting 
Myr; the BATSE sampling distance 
kpc).
In high-velocity neutron star models, the slope of the cumulative peak flux distribution for the brightest BATSE bursts and the PVO bursts reflects the space density of the relatively small fraction of burst sources in the vicinity of the Sun (d <= 50kpc). Therefore any spread in neutron star kick velocities, neutron star ages at which bursting behavior begins, the rate of bursting as a function of age, or the burst luminosity function tends to produce a peak flux distribution to -3/2, the value expected for a uniform spatial distribution of sources which emit bursts that are "standard candles." Figure 9 shows that a spread of less than a factor of 10 in the luminosity function, which is consistent with everything we know about gamma-ray bursts, is sufficient to produce agreement with not only the BATSE, but also the PVO, brightness distribution of bursts (Bulik and Lamb 1995). Beaming along the direction of motion of the neutron star can also reproduce both brightness distributions (Li, Duncan, and Thompson 1994).
The Galactic corona model predicts subtle anisotropies as a function of burst brightness, which are a signature of the model and may offer a means of verifying or rejecting it (Li, Duncan, and Thompson 1994; Podsiadlowski, Rees, and Ruderman 1995; Bulik and Lamb 1995). There is tantalizing evidence that such anisotropies exist (Quashnock and Lamb 1993; Lamb and Quashnock 1994), but these need confirmation using larger, self-consistent data sets.
It has often been stated that Andromeda, a bright galaxy similar to our
own Milky Way and lying only 
kpc away, imposes a severe
constraint on extended halo models (Hakkila et al. 1994; Hartmann
1994). This is true, however, only if one assumes that the burst
sources are distributed like the dark matter in the halo and that the
dark matter halo extends to arbitrarily large distances (Smith and Lamb
1993, Smith 1995). However, we know that the dark matter halo can
actually extend only 1/3 - 1/2 the distance to Andromeda because of
tidal disruption.
A similar statement has been thought to be true for corona models because in such models Andromeda must produce its own "wind" of high velocity neutron stars. Some of these will travel toward us, and when they produce gamma-ray bursts, BATSE should detect them.
However, Andromeda imposes no constraint if the bursts are beamed along the direction of motion of the neutron star, as some models posit (Li and Dermer 1992; Li, Duncan, and Thompson 1994). Then only the rare neutron star whose motion is almost directly toward us would be visible to BATSE. The few resulting bursts from Andromeda would always be swamped by bursts from the many high velocity neutron stars born in the Milky Way and moving away from us.
Even if the bursts radiate isotropically in all directions, detailed
dynamical calculations of the motion of neutron stars in the combined
gravitational potential of the Milky Way and Andromeda show that an
excess of bursts toward Andromeda is not detected until one samples
distances 
kpc from Earth (see Figure 10)
(Podsiadlowski, Rees, and Ruderman 1995; Bulik, Coppi, and Lamb 1995).
Thus there is ample parameter space (BATSE sampling distances 
kpc) for a population of sources in the
Galactic corona.
A larger sample of BATSE bursts or a more sensitive instrument might reveal an excess of bursts toward Andromeda. If so, this would constitute definitive evidence that the bursts are Galactic in origin. However, if no excess were detected it could be due to beaming of the bursts along the direction of motion of the neutron star and therefore could not be taken as definitive evidence that the bursts are cosmological in origin.
Where do we stand in weighing-up of evidence so far? Clearly, the cosmological and Galactic hypotheses are both consistent with the sky distribution and the brightness distribution of the BATSE bursts. Quite frankly, the two hypothesis are indistinguishable in this respect. Therefore we have to appeal to other evidence.