Data Source of layer changing after copy/paste in Table of Contents of ArcMap?

This appears to be related to the map document's (MXD) default database and relative paths. See the ESRI Help for details on relative paths. Relative paths are generally a good thing. I'm not sure if this would be a bug, but is certainly a gotcha.

The resolution is to uncheck the "Store relative paths..." option in the map document properties of the source MXD, File->Map Document Properties...->Pathnames. You should then be able to copy the layers to the destination MXD and maintain the absolute paths. Once you are complete you can switch the source MXD back to relative paths.

An alternative solution would be to set the default database for the two MXDs to the same gdb. This is also accessed from the same Map Document Properties window.

For myself, I prefer to to use UNC paths for network resources. UNC paths largely eliminate issues related to map drives, etc. that can crop up in multi-user, multi-computer situations. UNC paths are not fool proof, but they help.