The blog has comments about that family, including that man explaining things.
Apparently his wife was the one to ask, being bisexual and poly, if he'd be okay with her having a girlfriend. They ended up agreeing on a closed triad.
The first girlfriend didn't work out for the triad but his wife decided she didn't want to break up the relationship between the girlfriend and her husband just because he didn't work out with her.
Then they had a second "try" for their triad.
The original plan was a closed triad (with nobody allowed to have sex with anyone outside of it) and it ended up slightly different, but still there was no plans to add more people to the relationship if the triad worked this time, it would be the four of them, and that's it.
So while they're not allowed to have sex with other men, he's not allowed to have sex with people outside the triad+1 too. And considering he doesn't like men, a men can't enter their relationship since the basis was that everyone was with everyone.
I might have some details wrong, but the comments on the blog linked were, I feel, very interesting. It also seems they decided not to show several of the filmed families because they were too "normal" (I guess not enough "drama" to show on TV).
Also, at the time of the comment on the blogs the children knew about the relationship.
Anyways, I think you can always expect documentaries like that to select and twist as much as they can to fit the point they want to make. It wasn't in their interest to explain exactly how the relationship worked since they liked the "he's a polygamist" aspect of it, apparently.