Private organizations may also receive federal funding as well. Or, they elect to conform with AA for other reasons.
For e.g., if California legalizes m-h, which I know you have categorically opined against, universities especially state universities receiving federal funding will be subject to keep a m-h free campus to comply with terms of the fed fund as mh use including medial use is still illegal according to fed. law. However, some private colleges could opt to the same policy for reasons even though they do not get fed fund.
Those universities you mentioned highly likely receive fed. Fund.