the border gets drawn around it as a dashed black line. I don't want to even see this border at all.
That is not a Border. That sounds like the focus indicator which indicates the component has focus. All components have some kind of focus indicator to give feedback to the user.
Companies spend millions of dollars to have a consistent LAF, but if you really think your LAF is better then you can use:
checkbox.setFocusPainted( false );