Memberships not included in identity oauth endpoint

The docs state:

If you request memberships and DON’T have the identity.memberships scope, you will receive data about the user’s membership to your campaign. If you DO have the scope, you will receive data about all of the user’s memberships, to all the campaigns they’re members of.

However, if I set up auth without that scope (i.e. redirect the login button to/api/oauth2/authorize?response_type=code&client_id=<id>&redirect_uri=<uri>&scope=identity), then/api/oauth2/v2/identity?include=memberships returns an empty memberships list. Including the scope does work (the testing account has a membership entry for my campaign), but since I only need to fetch data for my campaign, I’d prefer not having to request access to all of the user’s memberships.

I know I can fetch members using the creator’s access token, but it would be faster to get the membership data (specifically currently_entitled_tiers, or at least the ID which I can use with /v2/members/{id}) via this endpoint.

I did double check the creator page I have the API client registered for.
Is there anything I’m missing?

Figured it out. Turns out who creates the API client matters (me being a teammate didn’t work while a client created by the team lead did). I think the docs should state this.