Both Acrobat Reader and the full version of Adobe Acrobat are able to work properly with freshly downloaded copies of the file.
It seems that Preview breaks something in the PDF file. If the same PDF merely is saved by Preview, the button functionality breaks, even if the buttons were not touched. Once the file is saved within Preview, even Acrobat can’t work with the buttons any longer.
It’s possible that there is an inherent problem with the file, but a freshly downloaded file works properly with Acrobat (both Reader and Pro), including the expected grouping behavior, while it fails with Preview and Nitro PDF Pro (formerly PDF Pen Pro).
Using any recent version of Acrobat and a freshly downloaded file, I was able to work with the radio buttons properly, i.e., if you click on a button, any previously clicked button is cleared.
Apple Preview does not work properly. I was able to duplicate the behaviors that @doug2 described, with the additional point that simply saving a freshly downloaded version of the file in Preview broke the button functionality.
Interestingly, Nitro PDF Pro was able to de-activate individual buttons after they were selected in Preview, but again, the logic connecting the behavior of the buttons into a group was broken. Complicating things even further, on a clean file, Nitro PDF was able to activate a button once, but then if another button was clicked, the first button was de-activated, but the new button did not change to active, and no further clicking would activate any of the buttons.
Maybe there is a bug in the original file, maybe there are bugs in Preview and Nitro PDF Pro causing this behavior, or maybe all of the above.
I’d actually prefer to use programs like Preview or Nitro for completing fillable forms instead of Acrobat, but in my experience, neither are nearly as reliable for that purpose, especially for government forms.