How to bend a rounded rectangle correctly on Illustrator?

I have a rounded rectangle with corner radius that completely covered the sides. See below:

I want to bend this so it is wrapping a circle. I can't seem to do it without messing with the caps.

I tried making this a brush and apply it to a stroke, here is the result:

Notice the caps are deformed.

Any idea?

Answer

You might consider this "cheating", but in that situation I would just apply a very thick stroke to a line and add rounded end caps:

You can always expand the stroke if you need to manipulate it as a shape