No, probably (s)he'll complete accept it and not even give a thought to its etymology. It's just the word that names that action.

At my workplace, we route video and audio over Cat5 to specialized PCs with capture cards, running software that records and then streams or uploads to a video content server where people can log into an account and view a list of presentations on a content management application.

They still email to ask if I can tape their upcoming event.

Probably about as crazy as your dad was when he was writing a file to disk, or when you post something on Facebook.