It sure must lead to 'misunderstandings' its like explaining theory of groups to a 2 yo.
In theory, encounters between us and a higher dimensional being couldn't even be experienced for us in lower dimensions (not in the same sence the being in higher dimensions would experience it)
Imagine an endlessly thin piece of paper being the universe of the 2d beings.
We couldn't even enter and be visible in their dimension, but they could exist and be visible in our 3rd dimension.
The easiest ways imaginable of a 3d object could enter and be visible in 2d universe is if you imagine an apple going throught a piece of paper frontally, its disection at the place it stops would be its shape to 2d beings, for it to pass whole through 2d space, it would change shapes from the moment it enters until the moment it leaves.
So a 2d being couldn't ever see how a 3d being actually looks like, and it couldn't even grasp the concept.
What you are suggesting is analogous with me trying to explain to my chicken that today is its birthday, which suggests us existing in the same dimension, with only very little to no difference in intelligence to higher dimensional beings.
Another theory is that there are only 4 dimensions, with the 4th one being time.
There are a LOT of interesting stuff to be discussed arround this topic, but it can best be done in person, over a bottle of oak aged fruit brandy.