spacetime dimensions - As 3-dimensional beings, do we really have 3-dimensional vision?

I was watching this video on YouTube of a high school student explaining perception in different dimensions, basically stuff he learned from reading the book Flatand.

At one point in the video, he says that as 3-dimensional beings, we can't really see our 3-dimensional world in the 3-dimensional way it actually is, because we have 2-dimensional sight. To illustrate this, he used a sphere, and explained how we can only know certain physical things about it by the way light reflects off of it. It seemed convincing, but thinking about it again right now I'm not sure that I'm really convinced.

He said in order to perceive our 3-dimensional world in the 3-dimensional way it actually is, we would have to be 4-dimensional beings, because then we would have 3-dimensional sight. But I always thought that as 3-dimensional beings, we have 3-dimensional sight and it's the 4th dimension that we can't see and have difficulty with mentally picturing.

But according to him, in order to see an $n$-dimensional world with $n$-dimensional vision, you'd have to be looking at it as an $(n+1)$ dimensional being in the $(n+1)$ dimensional world that encapsulates it.

Is this true? I was hoping on getting some clarification on this because it's kind of confusing.