As an experiment, I tried the Park Hyatt Tokyo for the dates of my next stay. The minimum daily rate quoted was overall about 10% above the minimum daily rate quoted on the Hyatt website. It appears the Five Star site rounded up lower-priced days to the highest priced day -- whereas the Hyatt website doesn't, it will show different rates for each day.
Of course, the Five Star rate in addition would likely be much worse than FHR or Virtuoso, and way, way worse than the corporate rate I have access to.
Not terribly impressive.