Not quite. I have had a lot of musical training and have a very good musical memory. I can write down songs from my head or hear a song and write it down later, depending on how complicated it is, usually with only 1-2 listens, or play it back, etc. I can visualize things in my head but it is a lot more abstract, or rather, harder to explain.
I think the person you're replying to didn't describe it exactly. It's not really about how good your memory is, I think. It's that no matter what, "replaying" the song in your head isn't going to bring about the same reaction as actually physically hearing music. It's like a simulation, a higher-order perception, thinking of yourself hearing it rather than willing yourself to really hear it in the same way as usual.
