Try something for me...
To an extent, I agree: strictly speaking, Web Browsers are not an operating system. But that's kinda missing the point: as with the hardware itself, these days the OS is becoming increasingly irrelevant.
So as an experiment, try unplugging your computer from the network. Go on, give it a go.
Now, what can you do with it? Bang goes media streaming (music/video/tv), access to server-configuration tools, music-downloading, web-browsing, email, instant messaging, online gaming, online apps (e.g. calendars, word processors), online storage, access to information sources (news, weather, search-engines, Wikipedia, etc) and several dozen other things besides.
Admittedly, ditching all of these is a great way of avoiding getting distracted. But at the same time, computers these days are generally used more as an access mechanism than as an actual tool; to pull out the obligatory car analogy, it's the difference between tinkering with the engine and driving to the shops.
And increasingly, we access online media and services via a single route: the web-browser. Even applications such as Steam and iTunes are little more than a wrapper to a browser-engine.
So yes: the browser is not the OS. But these days, does that really matter?