In ArcGIS Desktop 10.1, adding a basemap in ArcMap using the Add Basemap dialog box causes the coordinate system of the data frame to change to WGS 1984 Web Mercator (auxiliary sphere).
This is a known issue, and bug number NIM081490 can be used to check for status updates. Esri is working on a permanent solution to this issue. In the meantime, please refer to the technical article, “Adding a basemap changes the coordinate system of the data frame to Web Mercator (auxiliary sphere),” for more information on the issue and a workaround.
Chris F. – User Advocacy Group