That's the licensing agreement between the owner and the trademarks, and their customers for the use of the trademark.

But the American Halal Foundation could revise their definition of what counts as Halal, and then license the brand to a company that doesn't meet the current criteria, without asking for permission from anyone.

It's in your wording already: “the customer that the organization's standards have been followed precisely” (emphasis mine), nothing prevents the organization from changing their standards (well, maybe the licensing agreement with their customer brands does, but that's purely a contract thing and has nothing to to with the trademark per se).