What a blatant lie...
Carrot has been shown many times with the rest of the crew, acting as if she were part of the crew, like when Jinbei appeared in Wano and Carrot welcomed Jinbei just like the others, as if she were welcoming him to the crew to which she too belongs.
And when Luffy said they would drink after the victory in Onigashima, Carrot replied "Ou!" with the others, clearly as if she were already part of the crew.
Yamato, on the other hand, never even met the rest of the crew, was never even invited to join by Luffy, and when she said that she followed information that as Ace's brother, Luffy would let her, as Oden, board his ship, all he replied, with a face of disapproval, was that Oden was someone that everyone liked and that there's no way she was Oden.
And other than that, Luffy just accepted Yamato as an ally in the war. That's all.
That's totally different from the way how the others joined the crew.
In the others' cases, they received a very clear yes the moment they expressed the desire to join.
And considering how Oda has been doing some original stuff in this arc, such as making Sanji ask Robin to help him, to show how their personalities and principles are more complex than people may think, I won't be surprised if Oda makes Yamato actually ask another time to join the crew and receives a big NO as an answer.