First of all, why didn't you just put the diagram here? the FEN notation can be confusing in plain text, as well as prone to mistakes, especially if it's not in ready made format to be copied/pasted into another diagram.
Actually, he was right, whether or not that was his intention:
To explain that, it requires an understanding of what is called a "focing" move.
If, at a certain part of the game, I say that I can force a win by capturing a knight of yours, and after you capture back, I can mate you.
You can say "So, I won't recapture, but rather defend the mate, you haven't forced a win". Alas, yes I have:) Winning a piece is the same as winning the game beyond beginner level. I have seen many forcing sequences in different books over the years leading to mate, many of them had a way to sidestep the mate.... with a completely losing position.
No, you either have to recapture, resign (after losing the piece), or keep playing a hopeless position.
If you keep finding yourself managing to win such positions with a piece down for nothing, it means you may be playing against weak opposition.
If you don't know how a piece is to be used to win the game, then you have something to learn which will really help you improve.
For example, in the first position you've given, (if it's without mistakes), after Qxd7, black can just reply 1.Qxd7 Qb8 and there's no mate too. Of course, black is just lost there, so there's no point in looking at that move. What's important is what happens if black tries to resist.
Dear ladies and gents, Former US Open Champion I.A.Horowitz in his book "Chess for Beginners, p.58, diagram 119" stated, regarding the following position: 3rr1k1/ppqbRppp/2p5/8/3Q1n2/2P3N1/PPB2PPP/3R2K1 That by capturing the bishop with White queen could get a forcing sequence which led to mate. He miscalculated in the middle of this so-called forcing sequence :-) The intermediary position is: 3rr1k1/pp1RRppp/2p5/8/5n2/2P3N1/PPB2PPP/6K1 with Black to move; Mr. I.A.Horowitz didn't see Black's e8-Rook could just slide back to f8, avoiding checkmate! Love, amntony