Nope, you're 100% wrong IMO.
If you don't have a robots.txt file it's obvious you're ignorant of internet spiders and the technology to control them, so an ABSENCE of robots.txt should by default block the crawler.
If there's no robots.txt, I think it's also valid check the index page for meta tags that control crawler activity as well, if these don't exist either, which don't on her site, the crawler should keep out.
Basically, the crawler wasn't invited in but it also wasn't blocked, so there's no defined permission granted either way. Politeness alone would dictate to err on the side of caution until the webmaster figures out they have no traffic and learn to install a robots.txt file with permissions and explicitly grant spiders access.
Think about how this works in the real world. Just because you leave your front door open on a hot day isn't an open invitation for someone to walk in your house and sit down on your sofa, it's still trespassing.