I had to do some research to understand what you're referencing (some basic info starting on Page 57 of this BPDA presentation), and, uh...what?
What that thing is, is a relative of the NSRL, previously discussed (in some form) in the NSRL thread, the Crazy Transit Pitches thread, or both (it certainly deserves to be in both). As I recall the discussion when similar ideas came up previously, the cost bloat was feared to be enormous, given the inevitable difficulty and expense involved in a water crossing. I don't know what you're referring to with the "NS folks" designation, but one of the issues such a tunnel would have compared to the NSRL proper is that it would sever the Green and Orange connections inherent to that route (and Back Bay is only a partial replacement given the lack of proper Green connection, and then only on the southside lines that stop there), and, worse, it would actively remove the Green and Orange connections from any and all Eastern Route trains routed into this tunnel.
It's a proposal best suited to collapse under its own weight. If you're going to built a transit tunnel under the harbor, it should be Green, with a connection between the Transitway and the Central Subway; end Silver's forced dependence on buses and the Ted Williams, let the LRVs serve Seaport transit and the airport, and have proper connections to the other lines and bootstrap the northeastern quadrant of the Urban Ring. That's still Crazy Transit Pitches territory (at least until Baker & Company are gone), but it's better than that idea.
Hoo boy...and of course this is the final meeting where they're preparing recommendations. Something that ambitious in scope should have silver-green conversion as a pre-req.