Training agencies like PADI have the ability to set rules that govern what happens during training dives. That is it.
They have no authority to set rules outside of training. They can only
recommend what divers do when they go out on their own. Even the 130 foot limit is only a recommendation. If you want to go to 150, there is nothing an agency can do to stop you.
There are organizations that can limit your diving, and those organizations frequently pretend they are required to set those limits by the training agencies. It is a passing of the buck of blame. For example, when I was on a Liveaboard in Australia, we were given two different rules that very much limited our dives, and we were told they had no choice but to implement those rules because they were dictated by PADI. After those rules were announced, I took the diving director aside (not wanting to make a scene) and called BS on it. In private, he admitted there were no such PADI rules and it was only company policy.
- Some governments set limits. For example, in Cozumel's marine park, you must follow a professional guide. The dive flag laws mentioned above are another example.
- Many dive operators set limits. It is now getting more and more common for dive operators to require AOW for deeper dives. If you want to dive with that operator, you must follow that rule.
- Some insurance companies set limits. For example, my wife and I are planning a major and very expensive trip in the coming year, and we looked into travel insurance. In one policy we looked at, we would not be covered if a problem was caused by a dive in excess of 130 feet. Since I regularly exceed that depth, I did not choose that plan. I instead chose the DAN travel insurance plan, which has no such limits.
Finally, a little note about the laws of logic. If you believe something exists, and others believe it does not exist, the burden of proof lies with you to demonstrate its existence. You cannot claim that unicorns exist and demand that others prove they do not. If you believe DAN has a rule limiting OW divers to 60 feet, then the burden is on you to show that rule.