First off, that whole 15 minutes thing is absolute bullshit. Maybe its a worst case if you were in truly deep thought over one of the hardest problems of the year. But most of the time you aren't, and it will be a few minutes Like around 1.
YMMV but whenever I'm stuck with half an hour from coming to work to a meeting or between a meeting and the lunch break or whatever I feel that time is exceptionally unproductive. Whether it's making a change or implementing something new or tracking down a bug I usually need some time to work out what it really does, what it should do and how I can do it with good code that's easy to maintain. Most botched jobs happen if I rush that, I can work quick and dirty but it builds technical debt. That I'd be three times as productive if I had an hour (15 vs 45 minutes effective time) doesn't sound too far off to me. I try to have a few "just do it" tasks ready for that, but typically they're not supposed to be my top priority. So if I had a PHB who wants me to work on that task and no other task until I'm done productivity and quality would suffer.
Secondly- your productivity doesn't matter. The team's does. Those interruptions- it means a team member needs help. They're blocked. Their productivity is at or near 0 until unblocked. If interrupting you costs 15 minutes from you but saves an hour for him, that interruption is worth it for the team. There are almost 0 of those interruptions that aren't a net gain.
Depends on how many of these interruptions are from your team and about work, not to mention if they've actually checked and read the documentation or is just asking because bugging you is easier than making the effort themselves. That said, answering simple questions or checking Bob's calendar to see if he's in a meeting doesn't break the flow for me, that I can push/pop off the mental stack. If I need to take 5-10 minutes to check/discuss/explain/investigate/show something though I've decided I'm already distracted so time to check my inbox and answer what I can now before they're at my doorstep. Sadly we're not big enough to have a support staff to shield us from the solutions we've developed so it's DevOps and most the users are one or two floors down.