How else would you suggest they maintain the infrastructure without turning the users back into the product?
* Website sends HTTP response header containing a bitcoin address
* Browser keeps a bitcoin wallet
* Browser shows a button to send bitcoin from said wallet to said bitcoin address
And that's it.
You need a fee because otherwise nobody will do (or is doing) the work to implement it.
Of course, with something this small and basically one-off, given the number of open source devs building bitcoin projects I'd be surprised if no one's done something similar already.