That has been true for us; our first SB win had three excellent banks in Thomas, Hill and Garrison.
Then of course our next one had a HOF as well as of course our last three all a HOF RB.
BUT on the other hand you notice that KC had not had one; to be blunt who has won a SB with a TOP RB in the last ten to fifteen years? AND yes it is a passing league; just not as much a one as some here claim.
IF you want to win it all you need a running game that takes the pressure off of the QB. You need a running game to take time off the clock to rest your D.
Personally I think you can do that without a RB taken in the first RD. When was the last 1 RD RB to win a ring?