I don't think that's entirely true, considering how advanced persistent threats are evolving faster than researchers can document them I suspect there are plenty of ways to corrupt iOS and plenty have been documented by Apple itself on their product security page... and by that reasoning anyone really could "jailbreak" a phone (remotely) and install whatever they wanted.
Moatads.com is certainly a distributor of malware... the link below is the report from threatcrowd.org which maps the various virus/malware/"corruption" the server transmits.
HTTPS://threatcrowd.org/domain.php?domain=Moatads.com
You may consider enabling restrictions and under Safari you can either block all websites except those you approve or choose the middle option to filter adult content which also lets you allow as well as block the websites you choose.
Clear your website data and try to monitor if it comes back and when it did so you can determine what site, if any, you visited that allows moatads to load on your device.