If the outlet box is grounded does the outlet have to be grounded

Why do you assume the outlet box is grounded? Just because it is metal?

For quite awhile now electricians have been running ground wires to outlets even when the outlet box is mounted onto metal conduit and the conduit is connected to the frame of the Main Service Panel.

The reasoning is that even though the conduit runs back to the panel, there is no absolute that a section of the conduit has not pulled apart and the ground is now broken.

So In my very humble opinion, I would run the ground wire.

I agree, grounding to a metal box is no where near as safe as running a ground wire.

IF a metal box is properly grounded a "self-grounding" receptacle is perfectly safe, although I typically don't rely on them myself.
Pretty much all residential grade receptacles are NOT self-grounding.

The rule is that a bonding jumper always be connected to the green grounding screw of a receptacle.

If the box is metal, connect that also.

If the metal box is grounded, then only a jumper from the box to the device is needed.

I do not think "self-grounding" receptacles should be discussed with DIY'ers, for several reasons, whether they (devices) work or not. Too many variables to deal with, potential for problems.