@jacebryan, hey there! Thanks for reaching out and asking about this.
Base permissions for an organization applies only to all members’ access to the organization’s repositories. This setting is unrelated to accessing team discussions.
About team discussions article describes what’s required for a member to view either a public or private post:
Any organization member can post on your team’s page or participate in a public discussion. Private posts are only visible to team members and organization owners, and public posts are visible to all members of the organization.
As for the 404 error, my best guess is that the person viewing it may not already be a member of the team that discussion resides in. If that’s not the case and you’re able to reliably reproduce this behavior on any organization, we’re keen to see a complete set of steps to replicate this so we can investigate further before contacting our engineering team for their input.