That depends on what somebody means when they say their goal is the black belt. If their goal is simply to obtain a black belt you can buy those at martial arts supplies stores where they go for about five dollars. If their goal is to obtain the knowledge and skill that the black belt represents that's a different story. When somebody says their goal is the black belt they could mean the ladder.
From what I understand about the conversation, the point that the instructor was trying to make by offering to sell the belt is that its not about the belt, the skill isn't in the belt, but I think that's obvious to most people. I want to point out something that no doubt you and everybody else here already knows, there is nothing magical about a black belt or any belt for that matter. Putting on a black belt isn't going to magically give you any skill. If you've good when you're wearing a black belt you will be just as good when you aren't wearing a black belt. Likewise if your skill is terrible when you aren't wearing a black belt it will be just as terrible if you put on a black belt, wearing a black belt isn't going to change anything. So I would think when most people ask about getting a black belt what they're talking about is developing the knowledge and skills so that they meet the standards for it.