I could actually see Fury's twisted mind deliberately setting up the second SHIELD and not telling Coulson. Each would have different purposes (compartmentalization), and wouldn't have a "need-to-know" about the existence of the other until they "accidentally" cross paths.
It would lend each group plausible deniability of the others actions, or something. Fury would know that Coulson would have the ability to put on a good face for the rest of the world, and present a better image of a cleaner SHIELD, with heart -- which needed to happen after HYDRA. But given Coulson's reaction to the Guest House program, Fury would also know that he might be incapable of doing some of the shadier secretive things that SHIELD allegedly needs to do. So he set up a secondary backup shadow organization.
Not that I absolutely think that's what happened, but it wouldn't surprise me.
"Even his secrets have secrets."
EDIT: While it could conceivably be Stark behind "realSHIELD", the reason I very much question this is because it's completely antithetical to Stark's character. He's disgusted by people keeping secrets. He's a terrible liar. It's a running joke in the MCU that his own security system isn't even that good ("security breach, that's on you!"). This is the man who gave out his address on public TV to terrorists, and plastered his name to the side of a tower. Meanwhile, "realSHIELD" is so secretive and shadowy, it makes Coulson look like the Freedom of Information Act.
