A player controls the character, and may advocate for that character out of game, but has practically zero control on the meta level. There are exceedingly few mechanics which grant that level of meta-control in D&D. Re-roll style luck, in some editions, is one of them.A player both plays the character and are advocates for the character's perspective/interests at a meta level, among other things. That is D&D and always has been. In fact, it is true for nearly every RPG. Really.
To say that it is D&D would be highly mis-leading.