The full text is paywalled, but from the abstract:
"Four examples of typical wild edible plants were evaluated (stinging nettle, sorrel, chickweed and common lambsquarters), and based on substantial equivalence with known food plants the majority of the bioactive components reported were within the range experienced when eating or drinking typical food stuffs. For most compounds the hazards could be evaluated as minor. The only precaution found was for common lambsquarters because of its presumed high level of oxalic acid."
There are also several animal studies suggesting a potential protective effect of stinging nettles against kidney stone.
Oxalic acid is a component of the toxin injected by the stinging hairs, but this is removed by cooking.
It's possible that there's confusion because older stinging nettle leaves grow cystoliths (hard mineral deposits in the leaves). Cystoliths are usually calcium carbonate. I'm not aware of any plant that produces oxalate salt cystoliths. If anybody has some hard evidence for the composition of stinging nettle cystoliths I'd like to see it, even though I personally only pick stinging nettles when they're in season and the leaves are still young.
Once the leaves are older, there are all sorts of oxalates, and you should really avoid them if you are sensitive to kidney stones.
These plants also absorb pollution very effectively, so keep in mind where you pick them from.