There is nothing in the Rules of Golf that prevents a golfer from switching to a different brand of golf ball (i.e., from a Titleist to a Bridgestone) on every hole on the course - so long as the change is made between the play of holes. (Rule 15-1states: "A player must hole out with the ball played from the teeing ground ...")
However, there is something in the Rules of Golf that says a tournament committee can impose such a rule and WGT has always used.
It's called the "one ball condition" (in the rulebook, it's in Appendix 1, Part C), more commonly known as the "one ball rule." As you probably know, all Tour events are played under the "one ball rule." And any rules committee may adopt the "one ball rule" for its competitions.
The "one ball condition" requires the player to use the exact same brand and type of ball throughout the round. For example, if you tee off the first hole with a Titleist Pro V1x, then that's what you must play throughout the round. You may not switch to any other brand of ball, nor even to any other type of Titleist ball. You started with the Pro V1x, so the Pro V1x is what you must use on every stroke.
If the "one ball rule" is not in effect, however, golfers may swap out different types of golf balls at any point in a round of golf, so long as the change is made between holes rather than during the play of a hole.
Revised: Before someone asks, yes the R&A has the same rule which covers everyone in the world except the United States and Mexico.