Would you mind if I stayed in touch?

Hi, just heard this exchange:

  • Would you mind if I stayed in touch?

  • Yes, of course.

Now, the second speaker clearly meant: Of course you can stay in touch. I wonder why she said ‘yes of course’ instead of ‘no, not at all’.

What do you think?

Many thanks,

TOEIC short conversations: Contacting the computer help desk[YSaerTTEW443543]

Do we need a comma?

I wonder why she said ‘yes, of course’ instead of ‘no, not at all’.

What I managed to unearth is:
"The phrasing “do you mind” implies that the person won’t mind. So either a yes or no answer is still means “okay, you can have what you asked for.” If B didn’t want to lend out the book, B would have to say something like “I’m sorry, it’s not mine to lend” or “I’m sorry, it’s promised to someone else.” If B said “Yes, I do mind, actually” it would probably be seen as rude.
…Well, like we’ve already said, either yes or no will mean you’re going to do it. It’s not a matter of grammar, it’s a matter of ettiquette. If you DO mind, you really are expected to apologize for minding.

I agree - yes I do mind sounds terrible to my British ears. We usually give excuses: Would you mind if I smoke in here? Answer: I’m sorry, it is not allowed.
Would you mind if I opened the window? Answer: I’d rather you didn’t because I have a cold.
Would you mind lending me your dictionary? Answer: I’m sorry, I need it myself but you can borrow it later. englishforums.com/English/Th … w/post.htm
Also: englishforums.com/English/An … m/post.htm

As I got it, both yes/no answers could really mean “I don’t mind” in English.