So here's the thing. What makes a Brewmaster a proper representation from the Monk spec? The fact that Blizzard themselves tie Chen DIRECTLY to the Monk class. It's official, it's canon.
It's not a case of fans just assuming there is a connection. Blizzard has officially cemented that connection.
Now, when it comes to Beastmaster and Hunter, it's the same as (Metamorphosis) Demonology Warlocks and Demon Hunters. There is no direct connection between these classes or Heroes. There is implied connections, and we even have that explained in Warlock Green Flame quest. But Blizzard has not officially said that Rexxar's brand of Beastmaster class is a subset of the Hunter class. Again, I'm basing this on evidence from the game or from official sources, not just tying in *what I think* the Beastmaster Hero is or could be.
If we're talking about what spec emulates and covers the theme of a Beastmaster, then yes I agree with you that a Hunter does this. But a Hunter is not a Beastmaster Hero just like a Warrior is not a Mountain King Hero or a Chieftain Hero from Warcraft 3. They're not. They simply cover the themes and emulate the gameplay, but a Warrior is itself a Warrior class and not anything beyond that.
As I said pages ago, it's the same as us assuming that dark skinned Dwarf customization options were Dark Irons. Blizzard never officially made that connection, so all we had to go on was assuming they were the same. It wasn't until Allied Races that we could *CONFIRM* that they actually weren't the same, and that dark skin Dwarves are just dark skinned Bronzebeard Dwarf options. And the official stance is still in the air about Wildhammers, even though we have new 'Wildhammer' customization options for the basic Dwarf. We don't actually know if those are 100% Wildhammers, there is no *direct* connection (as far as I am aware, I could be wrong if there is new lore behind these customizations that I am unaware of)