Looking at the game analysis you provided, you made at least two mistakes: a) you analysed f5 and called it "standard". I found three games that reached the position after 10...d6, and all three refrained from playing f5? Instead, they all castled and allowed Black to play f5.
b) You claim, without any real evidence, that the position is "completely equal. Look at the sorry state of White's e-pawn." Well, Beliavsky managed to win from that "completely equal position, and he wasn't alone.
You may have at least discussed that game to show where Black went wrong.
For those who don't know the game I'm talking about, it's here:
In his book on the Budapest Gambit IM Timothy Taylor recommends against 4...Bc5 against the Adler Variation (4.Nf3). He instead suggests that Black should play 4...Nc6 and try to transpose into a Rubenstein variation. He says this is both because the Smyslov-Spassky attack is a very strong idea for White, and also that if you try the rook lift plan (first used by IM Dolphi Drimer) of going a5-Ra6-Rh6 White has many easy ways to shut this down by provoking d6 or driving the knight back to the sixth rank and thus blocking the rook's path over.
But what if instead of lifting the a8 rook all the way over to h6, you simply open the h-file for the rook already on h8?
Furthermore, what if you can utilize the same aggressive f-pawn push by White that Taylor is afraid of in order to accomplish this?