Enter layout mode and open up Layout Setup...
Clear the "show field frames when record is active" option.
Yep, I did that, too....still can't stop the border from appearing for a split second when the radio button is clicked. I've tried various ways to clear the border (that is--to make it white to match the white backgrond I'm using), but the border around the radio button is also whited out if I do too much. It's not a big deal, but it's a bit distracting.
With radio buttons, I don't think you have an option unless you go all the way and not use radio buttons at all, using regular buttons with scripts to modify the value in the field and conditional formatting or something similar to show which value is selected...