Boss Yes, I would. Would you really find it intrusive for someone who shared your daughter's job and who cared about her asking gently about her life having explained that they wanted some anecdotes for a personal tribute?
Police officers interview people for a living. It's not all interrogation. Most of them are very skilled and sensitive, so why wouldn't they be even more gentle with someone close to them to make sure that everyone knew what a special person their daughter was?
But if they really said they couldn't talk, and no one else could either, then I'd just leave it rather than using words like chatterbox, which is demeaning. After all, if someone's every second word was 'fuck' you'd cut that no matter how nice they were, wouldn't you?
Gentle is fine, but again I'd want to know in what way they were gentle and I fail to see how someone would be offended explaining how their daughter comforted a grieving mother - which is sadly, all in a day's work for a police officer.
In those circumstances people often tell you so much you feel guilty for having to leave some of it out. Some of them remain friends long after the terrible event.
I can only imagine that those special officers weren't there and the ones uncomfortable with tears were.
If you can't bring yourself to understand that melody then it's a waste of time explaining it to you.