With all due respect, I believe you're talking past each other because you haven't defined your terms.
Jeff, I believe, thinks of what his students did in that scenario as one "peek" followed by one attack (or whatever term you prefer.) He would not use the term "second peek" because the second time they came around to where they thought they would be able to see the threat, they intended to engage it and remove it.
Since taking the "first peek" gave the threat the chance to reposition and thwart the students the second time they came around, Jeff would not agree that it was a "freebie" just because they didn't get shot as they took that peek.
Firearms Academy, on the other hand, is using the word "peek" to refer to each and every time the student comes far enough around the corner or out of cover to engage and be engaged. Therefore, the way he sees it, whether you peek once and then give orders from behind concealment/cover or engage the first time you break cover, you have executed one "peek." If you peek once and then go back to engage, Firearms Academy would maintain, then you have actually executed TWO "peeks" around the corner, so he believes it's important to make the distinction between that method and the "single peek, then commands" method he is advocating.
Now, you can both tell me how wrong all that is.
Also, I realize that "break cover" and "come around a corner" are probably not literal descriptions of what you would actually do there. . . . but I don't know a correct term for it, and I hope we all understand what I mean by those terms.