There's also evidence that human intelligent is due in a large part to runaway sexual selection (like a peacock's tail).

Thats an explanation that explains the increase in intelligence from apes to humans and my comment was a lot about that but the original disputed claim was

Simple Darwinian survival ensures that any conscious species that has been around for hundreds of thousands of years must have at least some capacity for correct cognition, however that is achieved.

And there are less complex adaptive behaviors that require correct cognition: identifying prey, identifying predators, identifying food, identifying cliffs, path-finding etc. I guess there is an argument to be had about what a 'conscious species' but that doesn't seem to be worthwhile. Also, there is a subtle difference between what human intelligence is due to and what the survival benefits of it are. It may have taken sexual selection to jump start it but our intelligence has made us far less vulnerable than we once were (with the exception of the problems we created for ourselves). Humans are rarely eaten by giant cats, for one thing.

The fact that only a handful of species have high intelligence suggests that there are very few niches that actually support it.

No species have as high intelligence as humans but lots of species of high intelligence relative to, say, clams. --- Okay, that's a little facetious but tool use has arisen independently throughout the animal again and again, not to mention the less complex behaviors mentioned above.

Are people really disputing whether or not accurate beliefs about the world are adaptive? Or that intelligence increases the likelihood of having accurate beliefs about the world?