I've gotten a long ways in my technical career from being able to ask sensitive questions. (In the business environment, I've focused more on them being "critical questions".) It has been really great for me, and I've tried to make it as painless as possible for others. It started simply enough.
For real business reasons, there are things that I either needed to know, or I needed to be confident that the other person either had the answer to or were were putting some serious thought to. I wasn't asking sensitive questions just to embarrass them. I expected them to give me an honest answer (and I helped make that easier if an honest answer wasn't forthcoming on its own). I learned that I could trust my team not to take any of my questions out of context, and they learned that I would never try to take their answers out of context either.
Here are the big takeaways as best as I've been able to pin them down: it is all about trust, personal motivation, and intention. These complications are multiplied by the number of participants (even in situations where one person is asking a question and one person is answering the question, but multiple people may be listening). The process is quick and painless when the trust between the participants is high, the personal motivation (at the cost of others) is low, the level of trust between everyone is high, and there are just the two people. (Can it get better than that? Surprisingly, yes. Consider when one of the participants is a benevolent all-seeing and all-powerful diety.)
I have to admit, I haven't read the full article. I'd be curious what dimensions of trust they recorded and how well it coordinated with their results.
If you've developed all those factors between all the participants, you can ask just about anything with the minimum of time wasted. As one or more of these factors break down, the more complicated the conversation becomes. Or the more process you need to introduce to smooth over the wrinkles. "Hey, I don't mean to embarrass you, but on the Johnson account it is more important to get an accurate documentation than to show any kind of regular process. See? Here is where we've been capturing this for everyone, and this is what's done with the information." (So then you see how something like transparency comes into play.)
I think it makes sense when you look at it in those terms. You also need to be asking questions work asking, and sometimes you're going to be asking questions that you don't want or need the answer to yourself. You might be asking to build up trust within a group of people, or you might be asking because you know that several people really would benefit from knowing something that they're too conditioned to do on their own. (This is where I started. And the key is that even if a question is confrontational, you must never ask in a confrontational tone. The tone of your voice and the content of your words have to reflect that you're asking because you need to know. Nothing personal, just business.)
Even still, I hardly consider myself the master. I've never written anything down on this, but this is the 10,000ft view of what I picked up up over the years. If you've spotted something along these lines in a book or an article somewhere, let me know. I'd like to compare notes.