at GM level it probably is 'unsound'. But it is not refuted.

yea he didnt say it was refuted....white just gets a better position after returning the pawn.

It isn't something a gambit player really wants....

refuation means forcing a loss, it doesnt mean getting a clear advantage, an opening like this is called a dubious opening, please get your vocabulary straightened out.

Theoretically, if White knows his theory on the Budapest, he is usually better out of the opening. I probably will blog this at some later point.  However, I can tell you that in the last couple of months, I have played the Budapest as Black against both FM Strugatsky and IM Formanek and have gotten very comfortable positions out of the opening in both. So my guess is that very few people actually know the theory that well. Which makes sense, because if you look at the percentages, how often is the Budapest played?

Unfortunately the aftermath is that I lost both games, but one was because of an endgame mistake that I got squeezed on, the other was a bad blunder in the middle game that cost me an exchange - but had nothing to do with the opening.

You do realize black can just play 8...Qa3, right?

It's played far less often then f6 and white wins 66.7% of the time in the chess.com database. I wouldn't say that black has had much success in that line.

Okay, rybka - (10...Nh6 Rybka 2.3.2a mp 32-bit  0.91 (depth 12)  11.e3 Ne7 12.Qc5 Nc6 13.Be2 Qb2 14.e4 b6 15.Qe3)

Mamedyarov, Gharamian, Moskalenko and Sulskis have had great results with the sharp 4...g5 line. I strongly doubt that none of them knew about Dzindzi's "refutation". Oh no, Dzindzi doesn't even mention that 4...g5 exists- hardly a surprise.

His Nd2 line is actually what I used to play as white a few years ago, but white's advantage is rather too minuscule if Black knows his stuff. IMO the plan of developing the Bishop via b2 has much, much more poison.