Figured it out finally...
Being a long time Win32 dev, I know Flex and Java were case-sensitive
languages, but I didn't expect that case sensitivity to carry over to
how they access the file system.
My flex apps had upper case SWF extensions on them.  By default the
ANT filesets are case sensitive, which was my first problem.  The
second problem I had was that the AIRTestRunner source looks for lower-
case "swf" extensions, which I'm not sure is 100% correct to do, but
I'll just go with the flow on that since everything is working
correctly.