I'm not sure everyone is talking about the same thing.
If you are running parallel phase conductors in separate conduits, then you size the EGC in each conduit per table 250.122. That may mean you are putting a #1 ground in each conduit, and those #1 grounds do wind up being in parallel. Nothing wrong with that.
But if you are talking about using smaller conductors in parallel to get an "equivalent" larger conductor that is required by code, then I would say that Smart$ references would probably prohibit that.
Maybe the Steelhead can clarify exactly what situation he is asking about.