Unclear whether state_key/sender match rule also applies for join -> join

From [the spec](https://matrix.org/docs/spec/client_server/r0.6.1#m-room-member):

> The user_id this membership event relates to. In all cases except for when membership is join, the user ID sending the event does not need to match the user ID in the state_key, unlike other events. Regular authorisation rules still apply.

However, this text doesn't distinguish between `join -> join` and `somethingElse -> join`, and neither does the transition table. Does this mean that a third-party sender isn't allowed for *either* actual joins or profile data changes, and that eg. "moderator changes someone's room display name" is currently explicitly not supported?

Start with the linked Matrix Client-Server specification section m-room-member and the membership transition table mentioned in the issue. Determine whether the state_key/sender rule distinguishes join → join from other transitions, then update the relevant specification wording or table so the supported behavior is explicit.

Written by the indexing model from the issue text.