The flaw is not in the term itself. It's in trying to apply a very broad umbrella term to define very specific relationship structures. The problem is in using the term to make assumptions. Which is why people shouldn't take such stock in calling or judging someone else's relationship as poly or not or even saying that their relationship is a "typical poly relationship" (which can fairly be interpreted as a judgement even if the intention wasn't to judge). Simply because two different kinds of relationships are being described under the same broad umbrella term, that doesn't automatically mean they should be compared to each other.
It's like saying a person who's married is more monogamous than a person who's dating. And then the married person taking offense or being hurt that the dating person is also describing their relationship as monogamous. And then a bunch of people jumping down that dating person's throat for bringing up that definitions can be broad. At least that's how I see it.