The article is unclear about what exactly needs to be enabled in order for the app to work, but I don't think they are saying they can hijack wifi even when it's disabled. An important quote from the article on this note is
"So while PDQ doesn’t require existing connections, it uses the existing wireless chips to send data across short distances, which could be useful during power outages or natural disasters. That means you can’t have your iPhone in airplane mode while using PDQ, for example, because then it wouldn’t be able to tap into its wireless chips."
"So while PDQ doesn’t require existing connections, it uses the existing wireless chips to send data across short distances, which could be useful during power outages or natural disasters. That means you can’t have your iPhone in airplane mode while using PDQ, for example, because then it wouldn’t be able to tap into its wireless chips."