Working my way backward through the chain of execution, I could see that IE recognized selectFiles. At this point, I thought to check the Adobe Flash Player version to ensure that it matched the version of the SWFUpload Flash component that I was running. Sure enough, it was outdated. Once I installed version 9 and restarted IE, everything worked as expected.
I haven’t tried this on IE7 under a pre-9 Flash Player version (and in fact I’m not entirely certain you can get an older version of Flash Player that will run under IE7), so this may or may not also be possible under IE7 as well as IE6. If you want to test for the issue, simply catch any exception thrown when called selectFiles and alert the user accordingly.