> If the user asks about a particular page and Perplexity fetches only that page, then robots.txt has nothing to say about this and Perplexity shouldn’t even consider it
That's not what Perplexity own documentation[1] says though:
"Webmasters can use the following robots.txt tags to manage how their sites and content interact with Perplexity
Perplexity-User supports user actions within Perplexity. When users ask Perplexity a question, it might visit a web page to help provide an accurate answer and include a link to the page in its response. Perplexity-User controls which sites these user requests can access. It is not used for web crawling or to collect content for training AI foundation models."