With overtightening, you can possibly shear a bolt, or force a loose fitting taper all the way on, so the spindle end is flush with the end of the tapered hole.
Im not sure what role grease plays in helping/hindering damage; consult your local religious leader for more details.

With splined systems you can cause damage. One of the systems (Shimano or Isis) uses a faced end to the splindle splines, the other, a tapered end, which can distort the crank if over-torqued.

There should be no need for excessive force. I make judicious use of foot power on the end of a spanner. Can you tighten to the correct torque by hand?