No, I didn't find that section - I found the sections on --branch and --remote, and man 7 gitsubmodules has no mention of branch at all as far as I can see.
man 7 gitsubmodules
If there's something more, I'd love a pointer!
On the opening page it briefly shows the branch config option:
path = <path>
url = <repo>
branch = <branch> // <-- magical
We use branches as versions, so each minor change to a submodule increments the branch property. We then run:
git submodule sync
git pull --recurse-submodule
...to make sure that everything is updated. You're right in saying that it doesn't seem too well documented though.
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