She thanked the officers for ensuring South Africans were kept safe and reminded them that they, too, were citizens of the country.
The footage was taken during a memorial service on August 20, four days after the shooting at Lonmin's North West platinum mine.
"All we did was our job, and to do it in the manner we were trained."
She said the officers were going through challenging and tough times, and assured them what had happened was responsible policing.
"Whatever happened represents the best of responsible policing. You did what you did because you were being responsible. You were making sure that you continue to live your oath."
Expert questioned on footage
SA Human Rights Commission lawyer Nokukhanya Jele cross-examined public order policing expert Brigadier Zephania Mkhwanazi on the footage.
She asked Mkhwanazi to comment on Phiyega's comments, and asked if it was not better to wait until after "you have applied your mind" to what happened before reaching a conclusion.
Mkhwanazi opted not to answer the question, and commission chair Ian Farlam agreed.
Farlam said whatever answer he gave, shy of completely agreeing with Phiyega, could put him in an embarrassing situation.
This was not really a matter Mkhwanazi could comment on, Farlam said.
170 police; 3 000 strikers
Earlier on Tuesday, questions were asked about police planning before the shooting.
Jele put it to Mkhwanazi that on the day of the shooting there were about 170 public order police and more than 3000 striking Lonmin miners on the site.
In Limpopo and in Gauteng, there were a total of 1 314 public order police who were not called in to help.
Instead, other less specialised officers were called in to help, some from much further away.
Mkhwanazi said: "Advocate, as you said, if they were available. As I indicated from the beginning there were other service delivery protest issues that were taking place [in other areas]."
Jele asked him if the decision not to call more specialised police immediately had been a fundamental flaw.
No discussion of police plan
Mkhwanazi said he was not part of the planning, and was unsure what the situation in the other provinces was at that stage.
"If there wasn't anything taking place there, this was going to be the easiest way to have members there as quickly as possible.
"Therefore, if they never called them because there was nothing happening there, really it can be some sort of a mistake."
Jele also asked why, according to minutes taken during a meeting before the shooting, there seemed to be no challenge or discussion of the police plan.
Mkhwanazi reiterated that he was not present at the meeting.
"[The plan] should be critically analysed. I was not involved. I'm not sure if it was done because I was not there."
The commission is probing the deaths of 44 people during an unprotected strike at Lonmin's Marikana mine.
Thirty-four striking mineworkers were shot dead and 78 were wounded when police opened fire while trying to disperse a group gathered on a hill near Lonmin's platinum mine.
In the preceding week, 10 people, including two police officers and two security guards, were hacked to death near the mine.