I know that most times when the airbags deployed, the airbag module usually had to be reset/reprogrammed (look at eBay for some descriptions). If you don't do this procedure, the airbag light will be on even though the airbag might have been replaced.
As to why anyone would disconnect the pretensioners, I have no idea. Maybe the belts became a little too touchy like what you are now experiencing?
The salvage title vehicles I have been around either have locked up belts, non-locking belts, or belts too sensitive to braking forces.