You would be correct some of the time, but not for the professional tours. The Rules do permit the Committee to implement a condition of competition that the player must use the same brand and model of ball for the stipulated round, and such ball must be on the approved list (page 138 of the Rule book).
Of course you mean "The Open Championship" (its correct name)? :) Even though the one ball condition is not on the R&A hard card, it has been in effect at previous Open Championships and I presume it still is. The R&A hard card applies to all the amateur events the R&A runs and they do not use the one ball condition in those events.
From the definition of obstructions - "an obstruction is a movable obstruction if it may be moved without unreasonable effort, without unduly delaying play and without causing damage. Otherwise, it is an immovable obstruction." The rock Tiger et al moved was not an obstruction, it was a loose impediment.
There is an anomaly in your response. While the USGA is the governing body which establishes the Rules of golf (along with the R&A), they do not regulate the PGA Tour. The Tour plays by the Rules of golf (as established by the USGA and R&A) and are responsible for enforcing the rules (including the one ball condition) on the Tour. I sincerely doubt that what you have posted is actually true - it does not satisfy the one ball condition implemented by the Tour.