That Budapest line is verbatim in the book, page 79, note 12. But no mention of an engine relating to it. I checked pages 1-7, 61, and 79.
Your idea of 9.Be3 seems very nice.
Edited: On second thought, 9...Nxd3+ 10.Qxd3 Qe4 looks equal.
One thing I've noticed in Kaufman's books is his claim of += for evaluations which my other software gives as =. Similarly Kaufman gives +/- versus +=. Not to say either one is correct or incorrect, but I think it comes down to how much "advantage" white is willing to be satisfied with. After 6...e5 black does have an IQP, at least nominally it's something to work with. I can imagine many Caro-Kann players being reluctant to take it on regardless of whether this particular position is equal or not. I think it's equal, but then again I play different IQP positions in my repertoire, for both sides. If Caro-Kann players don't like it and won't play 6...e5, that's a mild argument for taking up the Exchange Variation.
Another detail is in the lines Kaufman gives (I used the preview at amazon.com), whether or not black plays ...Qc7, all black's other moves are the same: ...Nf6, ...g6, ...Bg7, ...Bf5, ...O-O. The difference is against ...Qc7 white plays Be3, when black omits this white plays Bf4 and seems to get a little more out of the game. So, if black is *not* going to play 6...e5, it makes sense to play 5...Qc7.