Are you sure you understood that correctly?
Wifi is just a node for transmitting data. If what you said was true, then all the other nodes on the Internet (routers, switches, servers, etc..) would also have the capability to strip SSL encryption and to
see all encrypted data being transmitted. This would obviously render SSL useless.
What I believe you saw was something called a man-in-the-middle attack. It essentially redirects internet users from legitimate websites to fraudulent clones, usually designed to harvest user logins/cookies. Note that it doesn't allow a hacker to view previously encrypted data, it just redirects you to a page where they can harvest data you provide. So as long as you know for certain that your data is properly encrypted and that your connect to a legitimate website (easier said than done for the typical user), you should be safe.
MITM attacks can happen anywhere on the web, not just on public wifi. So users must always be vigilant.
Personally, I wouldn't do anything sensitive on public wifi.
This stack overflow post covers the topic better than I can:
http://security.stackexchange.com/posts/34799/edit
One more thing. A lot of web services will encrypt your password when it is transmitted but keep everything else on the session unencrypted. In this case the router can absolutely see everything you're doing but your password.