Is it normal that Organic Groups group creator is not automatically "Administrator member"?
I should have seen this myself.
In fact the answer is in the slightly obscure "OG Settings" (Config > Organic Groups > OG Settings).

In this there is an option called "Group Manager default roles" which is applied to every OG content type. This allows you to "Select the role(s) a group manager will be granted upon creating a new group"

Problem sorted!