“The AEC said that the radiation from the blasts was contained underground and did not pose a health risk to nearby residents.”
The radiation? Yes, of course it was (apart from a load of neutrinos, a matter of no consequence). The radioactive contamination, not so certainly, although in a salt dome far below the water table, pretty reliable probably. Probably. A fact they were conscious of:
“The Department of Energy shut down the Salmon test site in 1971, fencing the property off from the public and installing groundwater wells for long-term monitoring.”
The stone marker warning future generations not to drill at the site is the “joke” though. What’s the chance of that still being on the surface in say three hundred years, never mind a few thousand? It’s likely to be either deeply buried, or eroded away. One or the other of those processes occurs almost everywhere over time. (Most fission products will be largely gone in a few hundred years, but actinides, particularly isotopes of plutonium, won’t.)
There are possible ways such a site might leak radioactive contamination, in either the short or the long term, even if no-one drills into it. They seem fairly unlikely to happen, but it’s foolish to rely on such guesses.
It’s worth remembering that the quantity of radioactive fission products (and actinides) produced in a nuclear power reactor is hundreds or thousands of times greater than that produced in a nuclear explosion.