If I understand your use case correctly, you want to set it up so that only people in your team can see your team boards.
The documentation states that...
A team-visible board will be visible to members of the team.
Set your trello board to "Team Visible"! You can do this from the board (simply click the status next to the title)
This is a standard feature of Trello and not restricted to Enterprise :-)
If you want to give yourself some piece of mind and test this out you can do the following:
Note: You should get the same thing if try it with another user that is not in the team.
Hope this helps!
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