What an interesting coincidence, hats off to you if it was intended. The announcer seen briefly at the beginning of the the Fleetwood Mac clip is my favorite supporting character in the Bob Dylan movie Don't Look Back
, but I never caught his name before. So, a little searching later, I found out he is Alan Price, the original keyboardist for The Animals. To carry it further, Price's playing on "House of the Rising Sun" was integral to the smash success of the song, and I doubt Frijid Pink would have covered it without The Animals' version coming first.
Even more searching claims The Animals were not inspired to record their version because of Dylan's (doesn't say if the musician they were inspired by was inspired by Dylan's version), and the late Dave Van Ronk still seems a little bitter about the whole shebang.