Every outside shooter has his "spots". Spots are places he practices his shots over and over. A shooter tries to get to his spots for shots as much as possible.

An NBA team plays 1/2 of its games and takes most of its practices on its home court. The shooters' spots are consistent there and most of the practice shots are taken there.

In the playoffs, for most of the teams, only a small percentage of games and practices have been played on the "away" court during the season. Consequently, the outside shooters are at a relatively greater disadvantage when they are away. I suspect shooting outside of 15' is not nearly as consistent for away teams. (Someone with better access than I have to the statistics might check that out.)

Even great offensive rebounding is unlikely to make up for that difference.

Home team dressing rooms tend to be a little better than road team dressing rooms. Every little bit counts.

While the dimensions of the court (or field in other sports) may nominally be the same, it is a mistake to think that they are not unique in ways which can't be seen on TV or sometimes even from the stands. Larry Bird once spoke on the dead spots in the floor on Boston Garden and making sure he knew where they were both for offensive and defensive purposes. Some football fields are notorious for bad spots that are better known to the home teams than the road teams.

And finally, of course, there is the crowd. The crowd doesn't always make much of a difference, or shouldn't when we are talking about professionals, but it has to be easier to do something difficult when ten of thousands of people are supporting you rather than booing, cursing, and yelling at you. While officials are neutral, it is within the realm of belief to imagine that they are at times subconsciously influenced by the crowds.