Ron - latest version of everything: WordPress 3.4.1, plugin version 0.5.4.3. I have my WP installation on example.com, and several sites with their primary URLS on foo.com, bar.com and baz.com. Sites like a.example.com, b.example.com and c.example.com all work fine with the customizer, but any site like x.foo.com or y.bar.com does not.
Clearly what's happening is the Customizer is refusing to see, say, "afoo.example.com" (which is the default name for the site at a.foo.com) as a reasonable alias for a.foo.com, somehow. Somewhere in your code, an alias is being translated too early or too late.
Contact me on firstname.lastname@example.org and I'll point a couple of different domains at your test site of choice so you can see the problem in action.