Pasting Masks as paths has become much more complex in AE6. After drawing your path (in Photoshop, Illustrator, or AE) and copying it to the clipboard, paste it onto the appropriate layer. It will sometimes paste as a Mask, not a path (even if you select the word Position before pasting it). The solution:
With the layer selected, type M and select the Mask Shape property.
Cut to the clipboard by pressing Cmd+x (Ctrl+x).
Select the Position property and paste by pressing Cmd+V (Ctrl+V)Cmd+v (Ctrl+v).