I believe the Ship's Boat is specifically a Mongoose thing. I don't recall that specific an award anywhere else.
In Classic, Naval Characters had no access to any kind of ship from their career.
T:NE had a totally different ship acquisition system, but both enlisted and officers in the Navy got pretty good modifiers to contribute to the group's starting ship.
T5 also gives Ship shares as a mustering out benefit as a possibility for all Naval personnel.
But I also fully second Rinku's post. There's nothing in the rules that suggest that the Ship's Boat is Navy surplus vessel, especially because the actual definition is any TL 12 small craft up to MCr10 in value. Or 2 ship shares.
That's basically any of the small craft in the basic rules except the Modular Cutter (MCr0.11 too much!) or the Shuttle. And quite a few of the small craft in other books, especially the Small Craft Catalogue, unsurprisingly.