Not exactly. Think back to the original use of the Arneson example I had- wasn't D&D. It was the Banana Republic.
Now extrapolate that. If you have a group of people (players) and they are trying to accomplish something, and there is no party, and one person is a referee, then:
1. There are times when characters can convince other characters in the game to do something. It's like the game, Diplomacy. Or like talking to other players. You can influence what the characters do through conversing- either as yourself or in a role.
2. On the other hand, if you acting in a way that is not persuasive or engaging in the fiction, but in a way that is directly opposition toward another player's character, then you need a method of adjudication that is neutral. One way of doing this is through, for example, rolling dice and having a referee interpret the results (this is also classic wargaming).
Move this into the area of TTRPGs, and the distinction becomes simple- the DM (the referee) controls the NPCs (that means 'monsters' too). Attempts to influence NPCs, like PCs, should be made one way. Attempts to directly oppose them (such as by attacking them) are made a different way.
In saying this, I am not saying that this is necessarily the right way to do it.* But it's not just "convention." There is a very sound principle behind that historical difference.
*Other people have provided reasons to not employ that system, such as a desire to be more inclusive of players that do not have the same social skills.