James,
The only reason that the draw tooltip will not go away would be that the identifys draw tool is still active. You likely have the keepidentifyactive set to true in the IdentifyWidget.xml.
As far as where the tooltip is set, it is set by the Flex API and that is why you can not find it. There is a mechanism to change it in the 3.6 version of the API but the ability to change the tip in the viewer was not added in the the setMapAction function of the MapManager.mxml in 3.6. This enhancement has been requested by me and will be added to 3.7 version of the viewer.