I think more are using open source GIS that would be visible: how would you know (unless the organisation told you) if they were using Mapserver and PostGIS to serve map data to their desktop clients? There is no purchase trail for anything other than any closed source desktop software in use, no evidence from polling their web/Internet connections, etc..
We are working on a solution for a public sector client that utilises open source, but the front end webserver is still IIS, even if the maps and data queries are all done through open source software.