As I understood, this tool normally shows distance in the project CRS units, not the geodetic meters (despite it actually says the distance is in meters).
However, now I read (Section III, 4 - Measure some distances) that in the Measure Tool Options you can change the "Ellipsoid for distance calculation":
Does it mean it can actually finally compute correct geodetic distance?
However, I don't see this option in the QGIS ver 1.9.0-Master.