There certainly are zero-day exploits out there for Android and iOS. So the technology exists for this to be real. In fact there is a thriving black market where discoverers of these exploits can sell them to the highest bidder -- here is an interesting article on that topic.
That said, according to the above article, Android exploits sell for $30,000 - $60,000 and iOS exploits for $100,000 - $250,000. Nobody is going to spend that kind of money on the black market and then turn around and open a junk website where people can see if their "Daughter is still seeing that no good jerk" for $27.
Also consider that once someone starts waving a vulnerability around the internet like that, it's usually a matter of days until Google or Apple figure out what's going on and patch it. Vulnerabilities only stay vulnerabilities if you keep them secret (unless people are using a version of Android so old that it's not getting updates anymore, in which case they're on their own).
More likely, this is a scam where you pay them $27 for the privilege of getting your own phone infected. The main tip-off is that they want you to download and run their software -- and not even through the app store.