@Will it depends on what amount of "updating" you require. However, you can set up a "PublisherPlus" style role, which has all the privileges of a publisher, with the added Admin privileges from the Content tab:
That way, this super user can update other people's content.
From re-reading your question, it seems like you already suspect this. But the reason the post from 6 years ago isn't relevant is because you're looking at updating content, not the organisation site itself.
David
..Maps with no limits..