I'm not talking about probing questions, I'm talking about loaded questions and interjections. Emotionally loaded.
Here's an example. Imagine this (with an angry tone) "I don't believe this! You made us do this last year and it was a disaster!" (Several nods around the audience.)
The wrong response to an emotionally loaded question
If you were to answer with, "I didn't make you, and you're exaggerating..." then wave goodbye to your credibility even if your response is factually correct on both counts. How could that be wrong? Because you would have missed the emotion behind the words.
In tough speaking times, the elephant in the room is always an emotion. A feeling. Ignore it at your peril. Presenters most likely to lose the plot here are those who ignore a feeling and answer only the face value of the words. Usually, they're the presenters who cross their fingers and hope that no one will raise the awkward stuff.
Your credibility with an audience is heavily tied into how well you can show that you have some idea where they're coming from. And that place is always a feeling, not a fact.
The right response takes courage, but it's effective
Speak to the feeling, then to the facts.
You can do that with words, or tone, or both. A word response might be, "I know how frustrating that must have been... difficult for your whole team, yes? So, this year I've modified the system...". etc. Notice the two 'feeling' words frustrating and difficult? They show that you have empathy. (Yes, that's really what we're talking about here.) Show that, and they're more likely to listen when you get to the facts.
Sometimes, for the milder questions and interjections, you can show empathy just with your tone, and maybe a nod that says, I heard what you really said behind your words.
By the way, beware of using the word understand directly. The phrase "I understand how you feel" suggests that you can fully understand what's in someone else's mind. You can't. So the phrase raises hackles.
As I said, it takes courage, but your credibility payoff is terrific.