Radio buttons are kind of annoying. They always seem to have some little quark about them that doesn't quite seem to get us all the way there. Besides, they are gratuitous: if you need a single selection from several options, you can use a dropdown; if there are only two options, you can use a checkbox. (Checkboxes are more "natural" anyways, since you see these on paper forms all the time. Radio buttons always make me think of standardized tests.)
In any project I've been on, radio buttons have always needed to be shoved a bit to do what we needed. Once we needed the ability to have a radio button list that allowed you to clear the selection by clicking the selected radio button. A few times radio button lists have taken up too much real estate on the form. In InfoPath, they just a pain in general.
An article that describes the basic problem and a decent work around can be found here.
Setting "type" and "name" explicitly (like you do with any other input control) doesn't generate any runtime errors; it simply does nothing. In fact, it appears as though setting the innerHTML of control that will contain a radio button is suspect. For example, here's something I tried:
The first alert box was blank, and the second one was, given the first one was blank, correct! It's like IE knows about its own issue here, and works itself around it! So, I used the technique from the aforementioned link and was able to move on with my life...for about seven minutes.
Next, I noticed the same shenanigans with the checked property. I tried all of the following, but was unable to get the damn thing to check itself: