Hi Exuma
You have to weigh these things up OTB very carefully.
An attacking player would offer that pawn without much thought.
They have a history of offering such pawns (who was White?...Infact who were the players?)
he knows the coming defence is difficult for Black.
He will get play for that pawn.
Black may have just rejected it because he saw the difficulties and
after 0-0-0 theatened to take it.
(The threat very often being stronger than the execution.)
He may not have picked his through the maze and decided it was not worth a pawn.
(Also, I don't know, it may be a theorectical pawn sac by White.)
However Lasker (and we will meet him again in a minute) writes
any centre pawn is always worth a bit of trouble.
All these maxims, quotes and rules of thumb.
Each one appears to have a counter rule of thumb.
Is it any wonder we are running around like headless chickens.
Winter writes that he once thought for ages (35 minutes if I recall)
before saccing a piece v Lasker. Lasker ignored it and replied within a
minute.
After the game Winter asked why did you not take the piece. Lasker replied.
"If a good player offers a piece sacrifice after 35 minutes thought it must
be good. You can keep the piece I'll keep the 35 minutes."
Or words to that effect, I cannot remember it word for word. Lasker won.
So let us have a quick look at what perhaps Black saw...
(though I think they just said "No Thank You." without much thought.)
[FEN "r3kb1r/ppqn1ppp/2p1p3/4N2b/3P4/3Q1P2/PPPB2PP/2KR1B1R w kq - 0 12"]
12. Kb1 {Actually baiting the d4 pawn as as a trap.} 12... Nxe5 13. dxe5 Qxe5 14. Bg5 {14.Bc3 and 14.Bf4 come into consideration. and these two would also have to be looked at before nicking the pawn. This 14.Bg5 is the scarey line. Note if the White King was on c1 then Black could play Qxg5+ and Qd5 here.} 14... Qd5 15. Qxd5 {Black cannot play 15...cxd6 16.Bb5 is mate.} 15... exd5 16. Rxd5 {16...cxd5 17.Bb5 mate. But the attack fails to....} 16... f6 {Coming this far is not beyond a good player, A lot of Black players would have stopped after 16.Rxd5 thinking he has his pawn my King is very open. This is not worth it - I don't even get a pawn and reject it.}
This is the other line the Black player would have to look at.
[FEN "r3kb1r/ppqn1ppp/2p1p3/4N2b/3P4/3Q1P2/PPPB2PP/2KR1B1R w kq - 0 12"]
12. Kb1 Nxe5 13. dxe5 Qxe5 14. Bc3 Qd5 {The Qd5 defence as mentioned aove.} 15. Qe2 {Now where does the Queen go? 15...Qg4 allows 16.h4 and g4 winning the h5 Bishop.} 15... Qc5 16. Qd2 {16...Be7 allows 17.Qd7+ and 18.Qxb7 winning the pawn back and another bag of tricks is opened. So...} 16... Qd5 17. Qe1 Qc5 18. Qd2 Qd5 19. Qe1 {That may be forced if you want it as White. No knowing who was the Black player, or anything about the game except that Breyer was involved, maybe he did not want or needed more than a draw.}