Expected grafana_admin to allow editing of other orgs dashboards

We were very excited to have the grafana_admin flag - we expected to be able to set that flag on our org for our LDAP group and then each of us in that LDAP group would be an admin in every org (my team manages grafana for our enterprise).
In the past we had used a single user account that we had to log in with individually (and potentially conflict with activities). We thought this new grafana admin setting would alleviate that.
This was not the case. What is the intent of grafana_admin?

As a Grafana admin you can manage orgs and users via Server Admin - and thereby assign to yourself the Admin role for any orgs where you’d like to work with dashboards.

In other words, being a server admin doesn’t automatically make you a member of any (or indeed all) organizations. That membership is assigned separately.
Though I have to admit my memory is a bit hazy with respect to how organizational membership is best managed when LDAP is used.