Just because one person is in a V, it does not automatically mean that this person's two partners must be monogamous, nor that the V is closed (or polyfidelitous).
Their partners (the people who are at the ends of that V, or the "arms") can have other relationships, too, but those people in those other relationships just might not be involved with or even know that person who is the "hinge" of the V.
The V only refers to one specific group of three people, two of which are in a romantic and/or sexual relationship with one of them, but not with each other. So, one person can be in a V but their partners can be in different Vs or other configurations with other people.
Example:
Jane is the hinge person in a V with Jack and Joe. None of them are married, and they all live alone. Let's call that V #1. Jack is also in a relationship with Susie, who knows about and has met Jane and Joe, but is not involved with either of them. So, besides being one arm of V #1, Jack is also the hinge person in Vee #2 with Jane and Susie.
Susie is also married to Sam. So, besides being one arm in V #2, this makes Susie the hinge person in V #3. Her husband Sam has two girlfriends, Lacey and Tracey, who are involved with each other. Together, Sam is in a triad with Lacey and Tracey, as well as being one arm of V #3 with his wife Susie.
Now, either Lacey or Tracey could be involved with other people, too. Their triad is not closed (obviously, since Sam is married to Susie who is straight and not involved with Lacey or Tracey). Anyway, let's go back to Joe of V #1. He's involved with Jane, which makes him one arm of V #1, but Joe has a boyfriend, Jerry, so he's also the hinge person of V #4.
Jerry is married to Jeff, which means that, in addition to being one arm of V #4, Jerry is the hinge in V #5. Jeff, though, is monogamous with Jerry and has no interest in having another relationship. Even though Jeff is monogamous, he is one arm of V #5 because his spouse is polyamorous and in two Vs, but that's fine with Jeff because no matter how many people Jerry might be involved with, they are happy together.
See, it could go on and on and on. Some people refer to Vs that connect like this as "N" or "Z" relationships. And those can connect and make a whole string of Ns and Zs. You could call that a network or constellation. There are solo practitioners of poly, who prefer to keep all their relationships separate (as I do). So I would only be in Vs, that's it. I'm a straight woman and only date straight men, so I'm not gonna ever be in a triad of any kind. This means, I could have three boyfriends who are not involved with each other, which would make me the hinge of a "W," but that would not automatically mean they are each monogamous with me. Any or all of them might choose to be, but they all could have other relationships, as well.
There is no rule that says a V must have two mono people who are only involved with one poly hinge person, with no other relationships or dalliances allowed. Did someone tell you that? Of course, there are situations just like that, but it isn't the only way a V works. Keep in mind that not all triads are polyfidelitous (faithful only to each other), either.
Essentially, it is not the configuration that matters. It is how well each person manages their respective relationships, and whether each person in any relationship feels respected, valued, and heard, that matters.