Ah, actually, it's a model Thirteen, three-inch.
With all respect, Gator, you've twice referred to the revolver as a Model 19 three inch. That is indeed a fairly rare piece and demands quite a premium. In point of fact, though, the model 13 in three inch is also quite desirable. The vast majority of 13s and 65s - - the fixed sight magnum K-frames, were made in four-inch trim.
Little Wolf, the round butt K-frame three-inch .357 is one of the truly great carry revolvers. At 31 ounces, it is light for its power, but still controlable with magnum ammunitiion. It is compact, and extremely rugged.
As to its being an "FBI gun," that agency did begin acquiring the Model 13, three-inch round butt type in 1974. The later, mid-1980s purchases were likely the later, 13-3 versions. Unless there is some verifiable documentation that this particular gun was a Department of Justice/FBI purchase, then it must be considered just an FBI TYPE revolver.
I have one of the 13-2 pieces, a three-inch from 1981, and I'm very happy with it. I was fortunate enough to snag it for about $325 last year, a very decent price for a pinned-amd-recessed type. It is certainly of the proper era and model to have been one of FBI group. Its condition is too nice to have been carried as a field agent's sidearm, though. There are NO special markings to indicate it was a DOJ purchase, so in my mind, it is just a very nice carry revolver.
If you do have a chance to pick up one for around the price you mentioned, it would be quite a good buy.
Good luck to you
Johnny