I would almost be willing to bet that your cranks are loose. You say you tightened the fixing bolt, but was it with a short allen key or a full sized torque wrench with a hex wrench on it? It takes a damn lot of twisting with your wrist to get the proper torque. The fact that repeats 180 degrees off says to me that you seat the crank in one off-square orientation and then spin it 180 and can push it over to the opposite off-square orientation.
Also, I have no idea where the don't-grease-your-BB-spindle thing comes from, but it's never made sense to me. It will help your cranks seat to the appropriate depth at the proper torque (versus getting "hung up" by metal-on-metal friction). Jobst Brandt covers this and other points on proper crank installation here:
http://www.sheldonbrown.com/brandt/i...ng-cranks.html
(assuming square taper cranks)