However, I’ve discovered that not all flavors of MSIE9 are created equal. I’m guessing that the reason the browser on the left does not render the corners is because it sits on a 32-bit version of Windows 7. The browser on the right runs on a 64-bit version of Windows 7. (The hardware is 64-bit in both cases.)
This was having me pull my hair out until I remembered the OS difference. This post is written to help some other poor soul figure out why MSIE 9 is not rendered rounded corners like it’s supposed to!