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This is just laziness on Atlassian's part. They should simply remove access to the Trello boards associated with the SSO account.

See: Github - where you can SSO into your organization's repositories but this is completely separate from your personal repositories.

Problem is they don’t know which boards are part of the SSO org since both emails are on the same account.

A board is owned by the user. In my case, my boards are clearly created by email ending in @gmail.com and not @company.com