PHP is not the only Server side solution. But i highly doubt he can't use PHP. Because it's the most common server solution. What host should that be without a PHP installation?? 2 cents / month service???????
But as i said. With Javascript you can build up Browser Databases, and store and read data. So remembering your own actions isn't a big deal then. You can test this by yourself. Is the website remember your inputs the same on different browsers?
I mean, let's clearify all that for you. That's the way to start i think.
Maybe you came along the phrase "push and pull". Well that's more common for socket system and some type of AJAX. But basically all dynamic data exchange on websites is a "push and pull" system. Because you push some data to the server, while others read that data by pulling it from the server.
What is used behind the curtain to store that data (serverside PHP or ASP or whatever) and what store system is behind (database, filesystem and so on) isn't important so far. Important is, that the data can be stored, altererd and readed.
I said, pure JS can't do that. That's still true. But beside HTML5 DBASE Systems there is indeed another way which could be used by your buddys Website. And that is node.js with some modules i won't name them here, because they are highly risky and "in my opinion" "BAD WARE". With those modules you may write and read files on your server with "then" pure JS. But that's a suicidal road nobody would go voluntarily.
Because servers with such a systems can be injected, infected and even come hijacked. Two years ago a bigger company "some may know and remember who i am talking about, otherwise forget about it" lost a lot of data by JS hijacking.
So for that reason, to get back to toppic, your buddy is using some sort of server side language. If he tells otherwise, don't buy it.