I'm now convinced that this is an issue with Studio's implementation of FLV. I took the same project of my 7-month old son crawling, saved it as a DV-AVI, and then used the Any Video Converter that Emmett mentions in his "YOUTUBE and FLV" post to convert the DV-AVI to FLV. That FLV file *does* behave as expected in the JW FLV media player, it has the scrubber and the time countdown on the right side.
Until this issue is sorted out by Pinnacle I'll just save my videos as DV-AVI and use the Any Video Converter to convert to FLV for my website. It's more of a hassle, but gets me the results I'm looking for. Hopefully this gets sorted out soon.
BTW - should anyone from Pinnacle wish to examine the files, I've got both FLVs, the one created by Studio 12, and the one created by Any Video Converter that I can email out to you.
P.S. I've now updated all the Flash video on my site using the Any Video Converter, so the problem I described is no longer visible there, however I still have the offending FLV files in case anyone wants to see them.