It's more a general and broad guideline to give an idea of how it operates in its behavior.
"The fictional detail of the monster in the narrative" is up to your discretion and imagination, which I would like to imagine that you have.
I wish it was just a general and broad guideline to give an idea of how it operates in its behavior. But it's not. It's a
specific game building block that determines damage potential, movement, defenses and the type of things that are appropriate as far as damage riders go.
The fictional detail of the monster in the narrative is indeed up to my descretion, but when it is a Role A of Level X, it is going to have a certain DPR, certain defenses, etc., and if that constrains the range of non-contradictory fictional detail. And not because a lizardman warrior is supposed to be a certain thing in the stats, but because it happens to belong to the larger category of brute or soldier or whatever.
Pre 3.x monster design: What are the main characteristics of this monster? How deadly is it compared to a common man or a trained warrior? How tough is it? Now make stats that represent that. Monster uses a weapon? Do damage by weapon + bonuses.
4E monster design: What role is this monster? What level? Spit out stats based on the formula. Then tack on abilities or powers to give the impression that it's somehow different than every other monster of that type and level. Monster rules a weapon? Ignore that and do standard monster damage by level.
See the differences?
My experience with 3.x is too limited to comment on how that game handles things. I think it has more of a absolute framework approach like the rest of Pre4E D&D does.