Lol, where's the proof of this my friend?
You would literally have to let the web browser save a file on the system itself. This is again, a matter of allowance, and doesn't even have to do with a browser having access, nor a browser being corrupted. To be honest, I don't believe you can point me to a webpage that, by simply accessing it, would lead to a corruption of a Linux system. It simply doesn't exist.
Instead, what is compromised is at worst, the browser itself. It doesn't just hook into the linux system like that, as you tried to point out. It's a bit like a sandbox, and wont access a system like that. Now, most people use the browser for a good portion of the time they are on the system, so it may feel like their entire system is corrupt, but its not. Plain and simple.
Again, Linux is virus proof to the average user. Hence, even an average user does not need an antivirus on a Linux system. Thanks for reading!