If they spend 20 minutes writing an e-mail, is that 20 minutes of productive time? I bet it's really only 5 minutes of what is considered 'productive', because they didn't write the e-mail for 20 minutes, they edited for 15, checked other e-mail, etc.etc. When they go to a meeting and it starts out with niceties, and talking about progress updates, etc. etc. Is that 'productive'? Necessary, yes, but productive? No.
We need to look at programming the same way. When I'm setting up my environment, I'm not being productive. When I'm researching a bug I'm fixing, I'm not being productive. When I try a fix and it doesn't work, I'm not being productive. When I'm looking up the most efficient way to write a method, I'm not being productive.
When I'm completely focused on coding, I'm at my most productive. I use a pomodoro timer, and if I really pay attention, I'm hopefully productive for 20 of the 25 minutes. If I get a few of those a day, I'm happy. That's the productivity of our job.
The sad trap I fall into is that if I've been productive for 4 hours in a day, I normally stop being productive, rather than continuing to push through, which I know I should do.