"What ethics rule is O'Brien referring to?"
Code of Federal Regulations, Title V, §2634.401
Two characteristics of the qualified trust assure that true “blindness” exists: the independence of the trustee and the restriction on communications between the independent trustee and the interested parties. In order to serve as a trustee for an executive branch qualified trust, an entity must meet the strict requirements for independence set forth in the Ethics in Government Act and this regulation. Restrictions on communications also reinforce the independence of the trustee from the interested parties. During both the establishment of the trust and the administration of the trust, communications are limited to certain reports that are required by the Act and to written communications that are pre-screened by the Office of Government Ethics. No other communications, even about matters not connected to the trust, are permitted between the independent trustee and the interested parties.
Code of Federal Regulations, Title V, §2634.405
... a proposed trustee is independent if:
(1) The entity is independent of and unassociated with any interested party so that it cannot be controlled or influenced in the administration of the trust by any interested party;
(2) The entity is not and has not been affiliated with any interested party, and is not a partner of, or involved in any joint venture or other investment or business with, any interested party; and
(3) Any director, officer, or employee of such entity:
(i) Is independent of and unassociated with any interested party so that such director, officer, or employee cannot be controlled or influenced in the administration of the trust by any interested party;
(ii) Is not and has not been employed by any interested party, not served as a director, officer, or employee of any organization affiliated with any interested party, and is not and has not been a partner of, or involved in any joint venture or other investment with, any interested party; and
(iii) Is not a relative of any interested party.
Is this a rule that requires the president to put his assets in a blind trust?
No. This is a specification of a "qualified blind trust".
However, there is a rule that federal employees must, when facing possible conflict of interest, either disqualify themselves from that issue, or divest (a qualified blind trust can fulfill the divestment requirement).
But The President and Vice President are exceptions to the rule.
Code of Federal Regulations, Title V, §2635.102
Employee means any officer or employee of an agency, including a special Government employee...For purposes other than subparts B and C of this part, it does not include the President or Vice President.
U.S. Code Title 18 Chapter 11 § 202 - Definitions
Except as otherwise provided in such sections, the terms “officer” and “employee” in sections 203, 205, 207 through 209, and 218 of this title shall not include the President, the Vice President, a Member of Congress, or a Federal judge.
The reasoning behind excusing the President is that, requiring him to disqualify himself, could prevent him from fulfilling his constitutional duties.