Multiple Sources Already Answered This Question

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  House Armed Services Committee Republican Staff Report

  “There was no ‘stand down’ order issued to U.S. military personnel in Tripoli who sought to join the fight in Benghazi.”
  Source: House Armed Services Committee, Feb. 10, 2014
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  Senate Select Committee on Intelligence Bipartisan Report

  “The Committee has reviewed the allegations that U.S. personnel, including in the IC or DoD, prevented the mounting of any military relief effort during the attacks, but the Committee has not found any of these allegations to be substantiated.”
  Source: Senate Select Committee on Intelligence, Jan. 15, 2014
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  Commander of Special Operations Command Africa

  Rear Admiral Brian Losey addressed this allegation first in a briefing before the House Armed Services Subcommittee on Oversight and Investigations in June of 2013, and then again in a transcribed interview with Congressional staff in March of 2014, where he stated: “There was never an order to stand down. The order, as I communicated it to the director of operations, was to remain in place and continue to provide security in Tripoli because of the uncertain environment.”
  Source: Transcribed Interview with Congressional Staff, March 14, 2014
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  Commander of the Four-Person Special Operations Team in Tripoli

  The Commander of the four-person Special Operations Team on the ground in Tripoli addressed this allegation twice, first before the House Armed Services Subcommittee on Oversight and Investigations in June of 2013, where he stated: “Madam Chairman, I was not ordered to stand down. I was ordered to remain in place.” He further explained that if his team had left on the plane to Benghazi, “it could have been catastrophic” because “The Special Forces medic was instrumental in providing the support to the wounded that returned. We would not have been in Tripoli in order to provide that support if we would have got on the plane. The decision by my higher headquarters to not get on that plane was the correct decision, in hindsight.” He again reaffirmed his statements during a transcribed interview with Congressional staff in March of 2014.
  Source: House Armed Services Subcommittee on Oversight and Investigations, June 26, 2013
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  AFRICOM Commander General Carter Ham

  General Carter Ham confirmed to congressional staff in his transcribed interview that the decision to keep that team on the ground in Tripoli was made by the Commander of Special Operations Command Africa, Rear Admiral Losey, and explained: “I do agree with Admiral Losey’s decision. At the time, the situation in Tripoli was very uncertain. There was a real concern, significant concern on the part of the Embassy that the Embassy and its personnel in Tripoli might be threatened. And so there was a necessity to make sure there was adequate security there.”
  Source: Transcribed Interview, April 9, 2014
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  Chairman of the Joint Chiefs of Staff General Martin Dempsey

  General Dempsey testified before the Senate Budget Committee in June of 2013 that “they were not told to stand down,” but instead that “the mission they were asked to perform was not in Benghazi but was at Tripoli airport” because “they would contribute more by going to the Tripoli airport to meet the casualties upon return.” General Dempsey explained: “By the time they contacted their command center in Stuttgart, they were told that the individuals in Benghazi were on the way back and that they would be better used at the Tripoli airport because one of them was a medic, that they would be better used to receive the casualties coming back from Benghazi, and that if they had gone, they would have simply passed each other in the air.”
  Source: Senate Budget Committee, June 12, 2013
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  Accountability Review Board Vice Chairman Admiral Michael Mullen

  Admiral Mullen told Congressional staff in his transcribed interview that the Special Operations Team Commander “was given direction to hold in place. There was never direction given to him to stand down.” He added: “an untold story here is the heroic efforts of the medic actually on that airport coming from Benghazi to Tripoli, which there are those that believe kept a couple of those wounded alive.”
  Source: Transcribed Interview, June 19, 2014
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  PolitiFact

  Politifact ruled Rep. Chaffetz’s claim to Fox News that “we had people that were getting killed, we had people who are willing to risk their lives to go save them and somebody told them to stand down” as false, based on the testimony of Gregory Hicks and the Accountability Review Board report.
  Source: Politifact, May 6, 2013
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  Select Committee Member Martha Roby

  After directly questioning the Commander about this claim, Rep. Roby released a statement that he “was not ordered to ‘stand down’ by higher command authorities in response to an understandable desire to lead Special Forces group to Benghazi in the wake of the attack. Rather, he was ordered to remain in Tripoli to defend Americans in anticipation of further attacks." She further stated that the Commander "acknowledged that had he deployed to Benghazi, not only would Americans in Tripoli have been left defenseless, but his forces could not have arrived in Benghazi soon enough to make a difference. These are important facts to clarify because there have been rumors and reports to the contrary.”
  Source: Press Release, June 27, 2013