> My understanding is that the offside rule is based on where the players' feet are, but based on this VAR is doing it based off of any body part. Do I have the rule right?

Not quite. Head, body and feet all count.

https://www.thefa.com/football-rules-governance/lawsandrules...

> A player is in an offside position if: any part of the head, body or feet is in the opponents’ half (excluding the halfway line) and any part of the head, body or feet is nearer to the opponents’ goal line than both the ball and the second-last opponent

> The hands and arms of all players, including the goalkeepers, are not considered.

> A player is not in an offside position if level with the: second-last opponent or last two opponents