Having led the process from the other side, the more often your name comes up in a positive light, the better your chances. Odds are that OPs work simply wasn't mentioned much by his peers. The person you are replying to was absolutely on the money.
Promotions aren't a popularity contest, but they definitely are a popularity contest.
Yet what you are saying is a bit different from the person I replied to (which I do agree with your final line). We also only have the information that the OP states. These are asymmetric information games so it is a bit naive to claim this for any response. Especially simple explanations.
Promotions aren't a popularity contest, but they definitely are a popularity contest.