I believe it's not that collisions (and gravitational interactions) don't happen when it's in a disk, but the galaxy as a whole has an overall rotational momentum about some axis, and collisions within the galaxy can't change that. This means that it can flatten along the axis, but it can't shrink in the perpendicular plane.
If everything were twice as close to the axis (as gravity would like it to be), it would need to be moving twice as fast to conserve rotational momentum, but that's faster than the velocity of a circular orbit at the new radius (assuming everything was in a circular orbits to begin with).
The same principle is why almost everything in the solar system approximately lies within a plane.