Another possibility is just plain old ArcMap funkiness.
If you take your layers into a new project you might be able to make it work
Previous problem - Attribute Transfer simply not transferring attributes. Solution to previous problem: create a new mxd and copy all layers over, start editing and create a new mapping. Works fine
New problem - Attribute Transfer tool switches source and target whereas it transfer attributes from target to source not from source to target. Solution to new problem: Same as before - create new mxd, copy layers over, re-map attribute transfer. Works fine
Conclusion: There is something broken in the mxd structure that causes the attribute transfer tool to malfunction. Creating a new mxd, copying layers over solves the problem until such time that it no longer works at which point a new mxd must be created yet again. Note: mxdDoctor does not correct the issue, a new mxd document must be created for this workaround.