BBGs do perfectly well in either brackish or freshwater, and I dimly recall having heard of at least one species being acclimated to marine conditions under lab conditions. I tried once, in a reef tank, but it wasn't a success (the BBG got eaten by an anemone... yikes!).
Oddly enough, most fish tend to ignore BBGs, but I still wouldn't risk it with GSPs. Even if the GSPs didn't eat them outright, It'd be hard getting enough food down to the gobies. Even with smaller fish, that can be a challenge, as BBGs are amongst the most finicky fish widely kept in the hobby. They make discus look like gluttons! Most BBGs that die in captivity likely do so not because of salinity issues, but because they starve to death.
Adding small fish to tanks with a single, well-established bigger fish usually doesn't work. It's too much like offering live food! In the situations where big fish and little fish coexist, they've often grown up together, so to a degree the bigger fish treats the smaller fish like scenery. Still, this approach often goes wrong, and I wouldn't recommend it.
The best tankmates for GSPs are robust marine fish such as damsels. There are some brackish water damsels, but unfortunately they're hardly ever traded (I've seen one species, once!). Still, if you raise the SG to 1.018, you can keep things like Dascyllus and Abudefduf spp., and these tend to work well with GSPs, given sufficient space. Again, adding a small damsel to a tank with an established GSP wouldn't be wise; best to remove the GSP, move all the rocks about, and then introduce both the GSP and the damsel together.
The old saying that "every puffer is different" does seem to apply to GSPs more than any other species. Quite possibly, it's the sexually mature males that are most aggressive, and it's also important to remember that both GSP species feed, in part, on the fins of other fish (at least in the wild). So there are a bunch of variables here like age, sex, and hunger that may play a role.
Cheers, Neale