Depends on whether stroke play or match play. As a general principal a player is responsible for any decision - unless made by an official.

Lets say there's a dispute over free relief.

Stroke Play

Play two balls (one dropped , one as it lies) and make it clear (before playing !) which will count if relief is available. Note both scores and clarify later. If you only play one ball and get it wrong you will get penalised later.

Match Play

The option to play a second ball does not apply and the players should find a solution and carry on. If they cannot agree the opponent must make a formal claim or objection (with reasons) there and then and clarify the point with the committe later.