Should they be allowed to carry? YES.
Should they actually carry? YES.
Is this a private organization? Yes.
Given that it is a private organization, do they have the right to institute rules and regulations they see fit? Yes.
Do you have to join this organization? No.
Do I agree with their decision to say that leaders can't carry guns? NO, but it is ultimately their say.
In light of the rising frequency of human/grizzly bear encounters, the California Department of Fish and Game is advising hikers, backpackers, hunters, and fishermen to take extra precautions and keep alert for bears.
We advise outdoorsmen to wear noisy little bells on their clothing so that the bears are not startled unexpectedly by a human's presence. We also advise outdoorsmen to carry pepper spray with them in case of an encounter with a bear.
It is also a good idea to watch for fresh signs of bear activity. Outdoorsmen should recognize the difference between black bear poop and grizzly bear poop. Black bear poop is smaller and contains lots of berries and squirrel fur. Grizzly bear poop smells like pepper and has little bells in it.

I happen to live with a bear (that's bear, not beer) biologist. The consensus is that in the lower 48 bear spray is actually quite effective. They are less predatory and encounters are likely to be surprise to all involved. Alaska is a different story; pack a big gun. Don't get me wrong; I'm not saying that I wouldn't carry a firearm where/whenever possible. But, don't completely knock the bear spray.
On a mostly related note, It is surprisingly easy to conceal a large handgun from clueless people. I went out on a spur of the moment trip to the local refuge last night with some friends. Before I left, I quickly swapped my 26 and crossbreed holster for my 20 and an owb holster. This is my typical open carry woods rig, but concealed was required for multiple reasons. I tossed on a t-shirt and Columbia shirt over it and called it good. It printed like crazy, but I wasn't that concerned. Turns out, 3 super liberal (sometimes you just have to take what you can get) people who don't have a clue about the locals have no reason to suspect someone in the car with them is carrying. I would have been called out if discovered; so, I know they didn't spot it. It also enforced the "concealed is concealed" policy. I mainly wanted to be prepared for 2-legged critters.