MSO is the master site for privileges descriptions, i.e. the pages listed on
/privileges. The text used on MSO is distributed to other sites on the network, and it's not possible to edit them individually on each site.
To edit those descriptions, a user needs to have 1000 reputation on Meta Stack Overflow. It's unlisted in the privileges descriptions pages, but I got it when I first had more than 1000 rep on MSO. The system doesn't care that a user is a trusted user on one of the "real" Q&A sites, and might actually be better suited to do this (based on own experience with the privileges) than someone who has 1000 rep on MSO.
Apparently, sending users to MSO to edit the descriptions is the standard response to "Please change the privileges documentation" topics on child meta sites. But even very high reputation users on other sites might not actually be able to do that, when they don't actively participate on MSO.
This behavior makes no sense and needs to be changed. The privileges description editing privilege should not be based on MSO reputation, but e.g. on network reputation (minus the account linking bonuses), or the highest reputation a user has on any SE site.
Alternatively, there should be a way for users that have 101+ MSO rep to suggest edits to the privileges descriptions. Currently, it's not possible to suggest edits on the privilege description pages with below 1000 MSO reputation. These low MSO rep users might already have all privileges somewhere else, so it doesn't make sense to not allow them to describe these privileges. The problem with this method is, of course, possibly too many bad suggestions from users having no substantial reputation anywhere.