I also don't think he was advocating nagging either, simply asking questions to get the candidate talking. If you "go dark" for 10 minutes, you're pretty much definitely stuck. Talking to the interviewer might get you unstuck. Staring at the whiteboard quietly probably will not.
This also isn't your day to day job so you have to keep in mind that these interviews are generally held to an hour length and you can't really give them 30 minutes for a single problem that wouldn't give you much insight into the person.
It also heavily depends on the culture of the company as well. So being able to communicate effectively and act under pressure is something that goes with pair-programming and code reviews.
To note, I have never had anyone ever leave an interview feeling bad about the company or our process, the interview is about the individual.
I still think it was pretty cool way of interviewing.
You're not bothering people while they're taking an expected amount of time to look at it. You're stopping a several minute silence after handing someone a basic loop and if statement.
For most positions we're talking about, this should not be a major problem. I found when doing something similar people either looked at me like I was crazy for giving them such a basic problem and after being reassured there was no catch answered simply and clearly, or just couldn't do anything. Followup questions about the code then went terribly (e.g. a JS contractor asking for £500+/day who didn't know what the difference between global and local variables was, why you should put var in front of things, etc).
These things are often good to weed out the incredible number of people who seem to have little to no coding ability at all for jobs where that's an obvious pre-requisite. I've also had people fail to solve a basic problem (roman numeral generator or reader) at home in whatever language they wanted, not even getting vaguely close. One person even sent in their broken version pasted into a word document.
Even if I solve the problem I'm walking out of that interview with a very negative opinion of your company.