The logical conclusion of your argument is that whether the fans cheer or boo should make no difference to the team. Unfortunately, that runs counter to the entire logic of football, in which home support is considered to be a major advantage as it encourages our players and intimidates theirs. By the same token, a lack of support or worse at home is bound to have a negative effect on the team. There is simply no escaping this logic, I'm afraid.
However good a player is, they are still subject to human factors. They can still use home support to raise their game as they would use any other advantage. Thus, the absence of home support makes a difference.