You're right, but both the MIT and the non-commercial portion of this new license explicitly grant the right to sublicense. It's not obvious to me that a free use case can't sublicense its use to a huge organization.
sublicense != relicense. You can't remove restrictions. All of the terms of the license would remain. That organization would still need to pay the fee.
If it was possible to re-license something in a way that removed restrictions from the original license, then no license would be worth anything. You could do a relicense end-run around any terms you wished.
(As another commenter said,) sublicensing does not permit you to grant any rights under the new license that you yourself have not been granted under the original.