Well, as the title stated, the Vikings did actually swap picks.
Proof: Take a listen to Speilman's comment in the Vikings draft room, starting at 1:21-1:30
For those who can't watch the video, I'll quote Rick Speilman himself.
Rick Speilman talking to Zygi and coach Frazier:
"We're flopping two. We're taking a second round pick and making it into a 1st rounder."
Welp, as in the eyes of Rick Speilman and our staff and a few commenters here, the Vikings did indeed swap our 2nd round pick for NE's 1st and essentially actually loss less picks than originally thought.