Teams that are up a goal go into a defensive shell; teams that are down a goal play more aggressively and get more shots. Everybody knows that, right? It's standard strategy. And yet, I was listening to the Sharks beat the Blues 5-3 the other day - San Jose was up three goals most of the game - and the announcers were incredulous that San Jose's 17-game streak of outshooting their opponents had ended.
The game score (and the time remaining in the game) has two major impacts on outcomes:
Trailing teams outshoot their opponents, while leading teams get outshot. The effect becomes more extreme the closer we get to the end of the game and as the lead gets larger. The most extreme situation is the empty-net end game, which significantly distorts overall results.
Shooting percentage displays some of the same trends, but not all. For most of the game, there isn't much of a connection between the score and a team's shooting percentage. It's only late in the game that trailing teams start allowing a lot more scoring chances per shot while not producing high-quality chances at the other end of the ice themselves.