It wasn't stated that that was the first thing he tried.
I've experienced router/modem issues where only certain sites were inaccessible until one or both pieces of equipment were restarted. I'd be interested in knowing exactly what happens to a router's software to make that happen.
I'd spitball a guess that it has to do with the firewall rules on the modem or router running themselves into a bad state. That would explain why a restart fixes it, since the state would be cleared.