Like that stops crazy fans to believe it anyway.
Fandoms also assumes that hate/dislike = sexual tension
"Just because two people dislike each other doesn't mean they're about to kiss, Sparkler."
The OP examples are how the recipient takes the inquiry, not necessarily how it was always asked.
eg. Quizzy askes Leliana how close was she to the Divine, Leliana then immediately takes that as innuendo. Quizzy phrased it in a way that Leliana could have just said she was like a mother to her. The fault is with Leliana's perception.
I am aware that I am not the sharpest tool in the wit/banter/innuendo/flirt(?) shed at all times.
But I remember those three instances particularly well because, at the time, I felt like that was exactly what was going on. Sometimes it makes me think that elcor have something going for them. Wouldn't things be easier if they were prefaced by 'Genuine Query. You and the Divine were close, weren't you?' [heated response] 'Aghast murmur. I simply wished to offer my sympathies.'
But now that I've had more time to think on it and gotten to know Dorian better, I've decided that those three do have legitimate reasons for jumping the gun and being defensive on those respective issues. So it's not necessarily that the Inquisitor asked a 'bad' question, but that those are just hot-button topics for those three and they're hard-wired, to some extent, to hear 'YOU WERE HAVING THE SEX, YES?' or 'YOU ARE A BAD MAN!' Though I thought that Dorian handled it well. I didn't feel scolded for a moment of innocent (from my perspective), friendly inquiry but I was made to understand rather effectively that that was not a topic he approved of discussing.