Puzzle 45263 mistake? or just me?

What did I miss? My solution is 7+ points better than theirs.

lichess.org/training/45263
training puzzle 45263

The puzzle's "correct" solution starts

1. ... axb5
2. Qxb5+ Kd6

Then the supposedly correct solution continues

2. Qxb4+ Ke6

and White wins Black's Bishop.

But I prefer

2. Nxe4+

Knight takes e-Pawn and now forks Black's Queen and King. Black may have believed e-Pawn to be guarded by d-Pawn, but Black's d-Pawn is pinned to Black's Queen by White's Queen along Rank 5. Black is in check, Queen is threatened by checking piece, which furthermore cannot be taken without revealing second attack on Queen. Thus, Black loses Queen: (A.) f Black ends check by taking Knight with Pawn (3. ... dxe4), then White takes Black's Queen with Queen (4. Qxg5); similarly, (B.) or (C.) if Black lets Knight survive and ends check by moving King instead (2. ... Ke6/7), then again White takes Black's Queen, this time with Knight (3. ... Nxg5). So:

if (A.)
2. ... dxe4 then
3. Qxg5
White wins Black's Queen exchanged for White's Knight;

or if (B.)
2. ... Ke6 then
3. Nxg5
White again wins Black's Queen, this time for nothing;

or if (C.)
2. ... Ke7 then
3. Nxg5
White again wins Black's Queen, again for nothing.

My solution (2. Nxe4+) wins Black's Queen and e-Pawn either for (A.) Knight or for (B.) or (C.) nothing; the "correct" solution (2. Qxb4+) wins only a Bishop. Thus my solution is at least seven, maybe ten points (Pawn-equivalents) ahead of theirs. Seven points can't possibly be just a judgment-call that my solution is "sub-optimal". I think it's an error.

But I don't claim to be a chess genius, maybe I misunderstood something ... WHAT did I miss? Does this happen often? Maybe there chould be forum-type comments linked to each training puzzle for this sort of discussion?

Thanks!

after Nxb5 Rb8 I can't see whites winning by any chance as good as Qxb5

After the puzzle ends, the obvious next move is taking their rook for a total of 8 points (rook + bishop), vs. 7 points (queen + pawn - knight).

I see, so, the THEORY is that the position after the "correct" solution actually is somehow better than the position after my suggested solution. I guess I can buy that theory, if you guys say so, who am I to question it?

If, however, that is indeed the case, it's just not a very good "puzzle" is it? A puzzle's author can't really guarantee that his preferred line (forego gaining 7 points in order to gain a supposedly theoretically better position, subjectively speaking) is actually "better" than some other preferred line (gain 7 points, despite positional supposed theoretical disadvantage, subjectively speaking). I mean, sure, crank it into an engine and see what the likelihood of victory is for each position forty moves down the line, but that's just not how people generally can operate when they're solving "puzzles." I mean, I don't dispute that the one line might be positionally better than the other; I just dispute that I can or can't be objectively determined to be positionally better.

I generally like the Li-Chess "puzzles" better than most other websites because they don't get you into a subjective position-versus-points "guessing game" for the solution. I prefer to try to be a more clear thinker than that. I would rather that my chess "puzzles" have criteria ("mate in two" as long as constructed properly is genuinely a "perfect" puzzle, no matter which site it's on) which are more verifiable.

Or, to follow on hoyabembe's comment, where he suggests that the taking of the Rook would be a required follow-on after taking the Bishop. In that case, shouldn't the entire puzzle progress to the point of taking the Rook to give opportunity for a "wrong" result if you don't take it?

Then again, like I said, I'm not really a master. My FIDE rating, if I had one, would probably be only in the 1550s to 1650s or around there (I'm guessing?), so if you guys have more helpful commentary I'd be happy to absorb it. Am I off-base about the nature of what a "puzzle" should be?

whoops correction:
"... I just dispute that it can or can't be objectively determined to be positionally better." (Replace "I" with "it" sorry.)

The higher difficulty puzzles are more clear in terms of the objective, maybe give those a try. Also, i believe the puzzles here are taken directly from actual games, so the 'fairness' of the puzzle is maintained by user ratings of the puzzle. Don't confuse this w/ the estimated difficulty of the puzzle which is based on the lichess analog of elo.

OK thanks for the pointers! I have to admit, I do learn from puzzles that are more ended about their objectives, since it's a new kind of problem-solving. In a mate-in-two puzzle, you always know whether or not you've found the solution, because if your potential solution turns out to be not a forced-mate-in-two then you haven't found it, duh. With a game-like puzzle, you think more like a game. Nobody walks up to the side of your over-the-board game and says "Now you should look for a mate-in-two move and avoid all other options." (Then again, I haven't ever seen a Lichess puzzle in which the solution was simply, "gee I oughta develop my Knight, since nothing else seems to be on tap right now, hence Nc3 = correct." That'd be a bit off-putting ...)

As stated by hoyabembe:
In your solution A, Black can save the Rook. In the correct answer, after Black moves out of check, the Rook is lost.

Pawn + Bishop + Rook = 9 points.
Two pawns + Queen - Knight = 8 points.

The correct answer is better by one point materially, and it has three white pieces hounding an exposed King.

Although I cant see that black has to give up his queen in a Nxb5 line, So I tried with the engine and it says equal, and I believe the engine xD, objectivly Nxb5 is much worse tha Qxb5+

@TInyKey. There is no Nxb5 line. After Qxb5+ Kd6, the OP is suggesting that Nxe4+ wins the Queen.