Cloudflare's test was to setup a dummy domain that had never been indexed, and had blocks in the robots.txt and the firewall.

Then when they asked perplexity it came up with details about the 'exact' content (according to Cloudflare) but their attached screenshot shows the opposite, it shows some generic guesses about the domain ownership and some dynamic ads based on the domain name.

If Perplexity was stealthily visiting the dummy site they would have seen it, as the site was not indexed and no one else was visiting the site. Instead it appears they made assertions about general traffic, not their dummy site.

Its not very convincing.