US Code says this (Sorry for the text wall, I posted the law as written):

28 CFR § 600.1 - Grounds for appointing a Special Counsel.

The Attorney General, or in cases in which the Attorney General is recused, the Acting Attorney General, will appoint a Special Counsel when he or she determines that criminal investigation of a person or matter is warranted and—

(a) That investigation or prosecution of that person or matter by a United States Attorney's Office or litigating Division of the Department of Justice would present a conflict of interest for the Department or other extraordinary circumstances; and

(b) That under the circumstances, it would be in the public interest to appoint an outside Special Counsel to assume responsibility for the matter.

§ 600.3 Qualifications of the Special Counsel.

(a) An individual named as Special Counsel shall be a lawyer with a reputation for integrity and impartial decisionmaking, and with appropriate experience to ensure both that the investigation will be conducted ably, expeditiously and thoroughly, and that investigative and prosecutorial decisions will be supported by an informed understanding of the criminal law and Department of Justice policies. The Special Counsel shall be selected from outside the United States Government. Special Counsels shall agree that their responsibilities as Special Counsel shall take first precedence in their professional lives, and that it may be necessary to devote their full time to the investigation, depending on its complexity and the stage of the investigation.

(b) The Attorney General shall consult with the Assistant Attorney General for Administration to ensure an appropriate method of appointment, and to ensure that a Special Counsel undergoes an appropriate background investigation and a detailed review of ethics and conflicts of interest issues. A Special Counsel shall be appointed as a “confidential employee” as defined in 5 U.S.C. 7511(b)(2)(C).

There must be some conflicting law or SCOTUS would not have taken Meese's amicus brief into consideration. Enter 5 U.S.C 7511(b)(2)(C):

5 U.S. Code § 7511 - Definitions; application

(a) For the purpose of this subchapter— (1) “employee” means— (A) an individual in the competitive service— (i) who is not serving a probationary or trial period under an initial appointment; or (ii) who has completed 1 year of current continuous service under other than a temporary appointment limited to 1 year or less; (B) a preference eligible in the excepted service who has completed 1 year of current continuous service in the same or similar positions— (i) in an Executive agency; or (ii) in the United States Postal Service or Postal Regulatory Commission; and (C) an individual in the excepted service (other than a preference eligible)— (i) who is not serving a probationary or trial period under an initial appointment pending conversion to the competitive service; or (ii) who has completed 2 years of current continuous service in the same or similar positions in an Executive agency under other than a temporary appointment limited to 2 years or less; (2) “suspension” has the same meaning as set forth in section 7501(2) of this title; (3) “grade” means a level of classification under a position classification system; (4) “pay” means the rate of basic pay fixed by law or administrative action for the position held by an employee; and (5) “furlough” means the placing of an employee in a temporary status without duties and pay because of lack of work or funds or other nondisciplinary reasons. (b) This subchapter does not apply to an employee— (1) whose appointment is made by and with the advice and consent of the Senate; (2) whose position has been determined to be of a confidential, policy-determining, policy-making or policy-advocating character by— (A) the President for a position that the President has excepted from the competitive service; (B) the Office of Personnel Management for a position that the Office has excepted from the competitive service; or (C) the President or the head of an agency for a position excepted from the competitive service by statute; (3) whose appointment is made by the President; (4) who is receiving an annuity from the Civil Service Retirement and Disability Fund, or the Foreign Service Retirement and Disability Fund, based on the service of such employee;** (Edit: This would explain why <ueller was allowed as special councel)** [(5) Repealed. Pub. L. 114–328, div. A, title V, § 512(c), Dec. 23, 2016, 130 Stat. 2112.] (6) who is a member of the Foreign Service, as described in section 103 of the Foreign Service Act of 1980; (7) whose position is within the Central Intelligence Agency or the Government Accountability Office; (8) whose position is within the United States Postal Service, the Postal Regulatory Commission, the Panama Canal Commission, the Tennessee Valley Authority, the Federal Bureau of Investigation, an intelligence component of the Department of Defense (as defined in section 1614 of title 10), or an intelligence activity of a military department covered under subchapter I of chapter 83 of title 10, unless subsection (a)(1)(B) of this section or section 1005(a) of title 39 is the basis for this subchapter’s applicability; (9) who is described in section 5102(c)(11) of this title; or (10) who holds a position within the Veterans Health Administration which has been excluded from the competitive service by or under a provision of title 38, unless such employee was appointed to such position under section 7401(3) of such title. (c) The Office may provide for the application of this subchapter to any position or group of positions excepted from the competitive service by regulation of the Office which is not otherwise covered by this subchapter.