My guess is she replied to you the way she did because of how you sort of snarkily said "You're welcome." Yes, you say you said it jokingly, but your response to this minor omission of a "thank you" kind of supports that her perceiving your "You're welcome" as snarky and rather passive-aggressive is probably accurate. You bear some responsibility for her response to your comment.

She's checking with the tech people because that's what you do when you are working for a company and a technical issue comes up. It isn't a matter of not trusting your input about the Skype thing; it's probably normal protocol to take such matters to technology when they come up.