If you’ve been invited to Buffer Publish as a user, your own Buffer account will be on the Free plan. You do not need to be on a Premium or Business plan yourself, as you’ll have access to all the Business plan features for any social accounts you’ve been invited to.
You’re also able to connect your own social accounts within the limits of the Free plan, which is up to three social accounts, excluding Pinterest. Any social accounts you connect will only be available to you, and cannot be shared with other users.
One caveat to this is if you’ve been invited as an Admin on the Business plan. Admins on a Business plan are able to connect social accounts to the Organization. In this case, when connecting a social account, you would need to make sure you're within the right Organization in the Org Admin tool.
If you notice that some of the social accounts you have access to have been locked, this will likely be down to the owner of the Business plan downgrading their account. When a Business plan is downgraded, the account is moved to the Free plan, on which fewer social accounts are allowed, and additional users are not supported. This is the reason those social accounts become locked for you.
In this case, you should chat to the Business plan owner and see if they had intentionally downgraded the account. It’s possible they didn’t know that downgrading their account would stop you from being able to access those social accounts.