This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
Hmm, that doesn't make any sense to me either--I've used Tiles without seeing the weird rendering you're seeing (although I haven't used Tiles for awhile).
Have you tried inspecting the element in Firebug? That might give you a clue to the CSS that's causing the issue. You could also check the actual DOM in both the Tiles and non-Tiles rendering to see if it's different, possibly causing the difference. You could also tweak the Tiles definition to see if that makes a difference--it might just be that the table cell isn't wide enough and collapses, causing the radio buttons to be wrapped.