Nice one, but billable work is - by definition - whatever you can get someone to pay you for. If that's the case, I'm pretty sure there are a lot of people getting paid to be on HN, or sleep under a tree with their phone on and being on call. That would be billable work too, and very productive if you consider productive to be "how much money I made".

And no, there isn't someone in the sky recording how many minutes you looked away from coding and deciding if you're an acceptable person or not. ;) The "work" vs "not work" is all in your head.