It is strange that SevenViolet have not responded yet about this line where he has been very implicated.

When I wanted to compare Rajmund's analysis with yours (MNb) today, I saw that the moves you give for White have been updated in Rajmund's page : 

1.e4 d5 2.d4 dxe4 3.Nc3 Nf6 4.f3 c6 5.Bc4 exf3 6.Nxf3 Bf5 7.0-0 e6 8.Ng5 Bg6 9.Ne2 Bd6 10.Nf4 Bxf4 11.Bxf4 Nd5 and now "12.Bc1!" instead of the previous given move: 12.Bd2. Is it a real improvment? I don't know, I have not checked it deeply yet. Same for the other line you are giving :

1.e4 d5 2.d4 dxe4 3.Nc3 Nf6 4.f3 c6 5.Bc4 exf3 6.Nxf3 Bf5 7.0-0 e6 8.Ng5 Bg6 9.Ne2 c5 10.c3  Nc6 11.Nf4 cxd4 12.Ngxe6 fxe6 13.Nxe6 Qb6 where Rajmund gives 14.cxd4 as improvement over 14.Re1.

What do you think about theses supposed improvements? Theses lines are all complicated, and need to be checked carefuly, I did not check all the lines seriously for the moment, but it is sure that it is a good line for Black.

According to SevenViolets and ArKhein the BDG is correct, as Black can get nothing more than equality. So I suppose they meet the Caro-Kann with the Von Hennig-Milner Barry Gambit.

1.e4
Via the BDG: 1.d4 d5 2.e4 dxe4 (or c6 of course) 3.Nc3 Nf6 (again: c6) 4.f3 exf3 (or c6 5.Bc4 exf3 6.Nxf3 Bf5) 5.Nxf3 c6 (Markovich thinks Bf5 more precise; does this imply, he thinks the HMG correct?) 6.Bc4 (I don't have faith in 6.Bd3 because of g6; Black can avoid this with 4...c6) Bf5.

1...c6 2.d4 d5 3.Nc3 dxe4 4.Bc4
Von Hennig's invention; it is much older than the BDG proper. See Von Hennig-Carls, Göteborg 1920.
Milner Barry played 4.f3 (as early as 1932), which can transpose, but offers Black some good independent options.

4...Nf6 5.f3 exf3 6.Nxf3 Bf5 7.o-o
7.Ne5 e6 8.o-o Bg6 =+ at least.

7...e6
7...Bg6 8.Ne2 Nbd7 9.Nf4 Nb6 10.Bb3 e6 11.c4 and X suggested Be7 =+, when SevenViolets gave 12.a4 as best.

8.Ng5 Bg6 9.Ne2 c5
9...Bd6 10.Nf4 Bxf4 11.Bxf4 Nd5 12.Bd2 o-o 13.a4 (13.Qe2 Nd7) and now, black can probably just play 13...Nb6 14.Bb3 Qxd4+ 15.Kh1 N8d7. Rajmund Emanuel gives 12.Bc1 h6 (Nd7!? 13.a4 N7f6 =+ MNb) 13.Nf3 o-o 14.a4 Nd7 15.Ra3; one sample line is c5 16.Bxd5 exd5 17.dxc5 Nxc5 18.Ne5 Be4 19.Bxh6 gxh6 20.Rg3+.

10.c3 Nc6 11.Nf4 cxd4 12.Nfxe6 fxe6 13.Nxe6 Qb6 14.Re1 Kd7 15.cxd4 Re8 16.Kh1 Qb4 17.Qe2 Bh5 18.Qf1 b5 19.Bxb5 (19.Bb3 Nxd4 does work now) Rxe6 20.Rxe6 Kxe6 21.Bxc6  Bd6 22.Bg5 Qxd4 =+.
This mainly is Bonsai's analysis from another thread. For details see:

http://www.chesspub.com/cgi-bin/yabb2/YaBB.pl?num=1083622751/0#0

It looks like Black can claim a =+, though play remains quite complicated.