You always have to run a ground ~. Rods will never do.
You must, must, must, in every case run a ground ~ from the main to the subpanel. Doesn't matter if you're running it 3 feet, to an outbuilding or up a space elevator. You have to run a ground ~ or you are out of Code. PERIOD.
Wait. Shouldn't ~ be the word "wire"? Not quite. With rare exception, metal conduit is a permitted ~. That is why you find no ground wires in your EMT work. I love EMT; it's easy, and it's clean. I run it even when I don't have to.
That said, I was caught by surprise by your anxiety about running a separate ground wire. The whole point of EMT is to make additional wires easy to add. I am thinking "why not just fish a ground?" What worries me is that maybe you erred when extending it. If you rendered the EMT no longer fishable, e.g. burying the cover of an LB elbow, that violates Code and you need to go back and fix it. Sorry. By the way, it's also illegal to assemble conduit around the wires. You must pull the wires, alter the conduit, then reinstall the wires, all of which is not that hard, and I do it all the time. This rule "keeps you honest" re: the other rule. If you did shove conduit over wires, pull the wires out (using them to drag in a rope) and carefully inspect them for physical damage, replacing as needed.
Adding a ground won't hurt. You are allowed to parallel grounds, just not anything else. And EMT in concrete can corrode, and that could break your ground connection.
Ground ^'s are a separate issue
Did you think I was going to say ground rod? Again, there are a couple of allowable substitutes.
- A metal water pipe, though this option is fading fast due to use of plastic pipes.
- An UFER ground, which is a ground rod built into a concrete slab using appropriate methods. Concrete guys won't do it by default, but make sure to stick a few in anything concrete. It uses the entire concrete slab (via the re-rod, and the fact that concrete is inherently moist). It's so good you don't even need to do an ohmic test.
By the way, the thing where they tied the EMT to the re-rod at intervals, is not an Ufer. That's just physically holding it in place for the pour.
The right word for all of these is "Electrode".
That said, you don't need an additional grounding electrode for a subpanel if you're still in the same structure, and breezeways count as "the same structure".
One more note on grounding electrodes. The connection between panel and grounding electrode must be a wire, this is one case where you cannot rely on conduits as ground paths.