From Les Sparks:

In general I believe it is possible to make changes to rent without HUD approval, but it is fairly limited in scope. Material changes have to be discussed first with the lender, then the lender can determine whether HUD should be involved. HUD’s own position used to be a little unclear. The following should make this clearer.

The new Borrower Regulatory Agreement indicates the following:

Actions requiring HUD approval
(n) Enter into any amendment of any contract or lease relating to the Project, except to the extent such contract or lease does not require HUD’s approval, including without limitation any amendment that (i) reduces the rent or other payments due to Borrower, (ii) materially increases the obligations of Borrower or the rights of the other parties to such contract or lease, (iii) materially decreases the rights of Borrower or the obligations of the other parties to such contract or lease, or (iv) alters any provision of such contract or lease required by HUD to be included therein.

The master lease indicates the following:
The Master Lease shall not be terminated prior to the expiration date thereof or assigned without the prior written approval of HUD. In the event of any assignment of the Master Lease, as a condition to such assignment, the assignee shall execute and deliver a regulatory agreement in form and substance satisfactory to HUD. The Master Lease shall not be amended without the prior written approval of HUD if such amendment would (i) reduce the rent or other payments due thereunder, (ii) increase the obligations of the Borrower or the rights of the Master Tenant, (iii) decrease the rights of the Borrower or the obligations of the Master Tenant, or (iv) alter any provision of the Master Lease that HUD required to be included therein. Copies of all amendments to the Master Lease shall be promptly furnished to HUD and the Lender.