I was reading this answer in my quest to see how possible adding grounds to my existing knob and tube house would be, and was suprised by:
Are you asking if it's OK to run a separate ground wire from the existing? The answer is no; all your wires have to be in the same conduit
I am far from an electrician, so I can't see what the problem is in having two outlets grounded independently. What is the danger?
If you're talking about the equipment grounding conductor, and not the grounded (neutral) conductor, then they may not have to "share" the same equipment grounding conductor.
This answer contains all the code references, if you want to give it a read. If your area has adopted the 2014 version of the National Electrical Code, you can share an equipment grounding conductor from another branch circuit, as long as both circuits originate from the same enclosure.
250.130(C) Nongrounding Receptacle Replacement or Branch Circuit Extensions. The equipment grounding conductor of a grounding-type receptacle or a branch-circuit extension shall be permitted to be connected to any of the following:
(4) To an equipment grounding conductor that is part of another branch circuit that originates from the enclosure where the branch circuit for the receptacle or branch circuit originates
