My dad says he is sure the tag cannot fall off on its own

Yes it can. All of my lost tags over the years were when gate checked and the one I lost the fastest was the metal screw attachment.

I suspect the gate agent radioed down to the ramp agents to instruct them to take off the luggage tag. Is that possible?

Doubt it. It's almost a guarantee that it's sitting in the cargo hold.

Your dad can order more diamond tags by getting in to his account.

He can order a new card but Delta won't replace bag tags... I know this from losing my tag during a gate checked flight and asking for it. It's a no go.

those tags can be used for upgrades so I am not surprised it got swiped

No they can't. Any upgrades occur because the ticketed flyer in the system is identified as an elite on the upgrade list. Showing a bag tag has no influence over whether you get an upgrade.