"Satisfactory assurances" refers to receiving sufficient guarantees or promises that something will be done or achieved to meet a certain standard or expectation. It means having enough confidence or certainty that a particular outcome will be satisfactory or acceptable.
Full definition
Obtain
satisfactory assurances in the form of a written business associate contract that its business associate would appropriately safeguard all ePHI in its possession; and
The HIPAA rules allow sharing PHI with HIPAA contractors and subcontractors assuming they have received «
satisfactory assurances... that the subcontractor will appropriately safeguard the information.»