People want to be trusted to do their job and be given the freedom to figure out the solution to whatever the challenge at hand is. Employers and supervisors want to see results that hit the target and make real progress on the big goals. I see the upper right quadrant- high freedom and high accountability- as the ideal to work toward, and believe you can't really achieve success in one dimension without addressing the other.
On the other hand you may have a team member who you have given a long leash, so to speak, but you have still not seen the results you want. In those cases, there is a good chance they may not understand what is expected of them, or understand the stakes of their work, or some combination of those two factors. This too would be an opportunity to recalibrate by negotiating clear expectations around what both sides value and need from the relationship. Aspiring toward the ideal of high freedom and high accountability can help ensure everyone gets what they need from the partnership.