Dennis Harwood,
On their scorecards, many clubs include the phrase,
"USGA rules apply"
"USGA rules apply with the folling local rules........"
"USGA rules govern play"
Hence, in your example, and additionally, for handicap purposes, the foursome could not agree to waive the rules.
I wonder, in stroke play, if the competitors could agree to play a provisional ball, declaring that ball as the ball intended for play in the event their decision to play a provisional ball is upheld.
If they were the only foursome in the stroke play competition, my feeling is that they would be upheld, but if there was more than one foursome, and not all of the foursomes chose the provisional ball alternative, I don't think they would be upheld.