I have this shape. When I add stroke and make the round the corner I still have the inner corners and they are not round.
The Rounded Rectangle tool leaves corners square inside, requiring the clever workarounds above.
But use the plain old Rectangle tool — with SQUARE corners — to make a rectangle. Then use Effect > Stylize > Round corners to set the radius of your corners. The corners will be round inside AND out! Counterintuitive, but it works.