What you're describing is normal functionality. Any member of the board will be able to delete cards and move cards. In order to restrict access, a user would need to be made observer of the board (only Business Class) and their limitations would be view board and vote (if enabled).
You’re invited to our first ever Trello User Groups Good news for current and aspiring Trello enthusiasts! We’re launching Trello User Groups so that you can network, share ideas, solve ...
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG
We're bringing product updates and pro tips on teamwork to ten cities around the world.Save your spot