Perplexity runs two crawlers, and the distinction matters more than usual: PerplexityBot respects robots.txt, but Perplexity-User — which fetches a page to answer a specific user's question — generally ignores robots.txt rules, per Perplexity's own documentation, because a human requested the fetch.
The practical consequence: a robots.txt Disallow will stop PerplexityBot from indexing you for Perplexity's own search, but will not necessarily stop Perplexity-User from fetching a page a user explicitly asks about. To control the user-fetch case you generally need server- or CDN-level rules, not robots.txt — which is exactly the layer a live crawler check tests. Confirm current behavior on Perplexity's official page.