Currently, the "Add Join" tool (ArcToolbox > Data Management Tools > Joins > Add Join), when used within Model Builder, only allows tables as the input to the "Layer Name or Table View" field.
It also does not recognize database connections already defined .
(There are apparently similar issues with "Select Layer by Location", and "Select Layer by Attribute")
Please add all data types that it would normally accept when used from within an MXD.