I have a SharePoint 2010 Enterprise installation with the Dec 2011 cumulative hotfix. It is using integrated authentication and is on SSL. I can access my site collection from outside the server in the browser and everything works fine.
When I try to publish an InfoPath form template to my site, InfoPath gives the error "The following web server does not appear to be running SharePoint: {same url that opens fine in the browser}."
When I try to open the site in SharePoint designer (from outside the server itself but also from a location where the site opens in the browser), I get the error "The server at '{same url that opens fine in the browser}' does not appear to have Microsoft SharePoint Foundation installed." I have client integration enabled on my web application for Windows authentication (the app is not extended).
Since these two messages are similar I assume they are caused by the same thing. Does anyone know what this might be?