According to the Rules of Golf:
17-1. Flagstick
Attended, Removed or Held Up
Before making a stroke from anywhere on the course, the player may have the
flagstick attended, removed or held up to indicate the position of the hole.
If the flagstick is not attended, removed or held up before
the player makes a stroke, it must not be attended, removed or held up during
the stroke or while the player's ball is in motion if doing so might influence
the movement of the ball.
17-4. Ball Resting
Against Flagstick
When the flagstick is in the hole and a player's ball when not holed rests
against it, the player or another person authorized by him may move or remove
the flagstick, and if the ball falls into the hole, the player is deemed to
have holed out with his last stroke; otherwise, the ball, if moved, must be
placed on the lip of the hole, without penalty.
Thus while it seems weird on WGT to be able to remove the flagstick when the player is far from the green, it is OK under the rules.
Actually I checked this old forum for advice on whether it is generally better to remove the flagstick or not, on any approach shot. I have seen lots of hole-in-one replays where the ball drops even though the stick is there, but I have also noticed on my own replays (alas, no holes-in-one) that when I had pulled the pin it is back in when I run the replay.
While the pin could deflect a good shot, on the other hand, if the ball was travelling fast enough to deflect it was probably also travelling too fast to drop in, so maybe it ends up closer to the hole after being deflected than it would be if it skipped over the hole and kept rolling.