Is there such a thing as "fringe" poly -- in analogy to "fringe" fandom? I think there is -- at least in the abstract. These are the people we (almost) all know about, and (mostly?) all accept; but may (some of us) feel a bit defensive, apologetic and embarrassed about. Some "mainstream" ("canonical"?) polys might openly question whether "the fringe" does The Cause more harm than good.
A discussion a few months back amongst some Unitarian Universalist polys revealed a basic disagreement about what constituted "poly". For some, it was anyone who was non-monogamous -- anyone with more than one sex partner. For others, it was a question of whether you formed "serious" relationships with more than one person. Some people took "poly" to include all varieties of consensual non-monogamy. So that "poly" people included "polyfidelitous" people, "polyamorous" people, "swingers", and perhaps even "cheaters". If the last group were to be excluded, it would be from a feeling that "cheating" is not consensual (as well as deceptive?).
But what about "don't ask, don't tell"? What if your husband tells you it's okay to have affairs -- as long as you don't tell him about them? What if your husband tells you it's okay to date other men, as long as you don't become "serious" about them (meaning -- he won't allow you to live with your boyfriends, or invite your boyfriends to live with you; or have children by your boyfriends)?
Many of us support the right of Mormon men to have several wives -- we merely object to the patriarchal view these men often have of those wives. We also support the right of Mormon women to have several husbands (which polygamous Mormon men generally consider an "abomination"!).
What about people who do not assert "veto power" over their partners? Are they poly are not? I think most of us would say "yes!"; but is that even if they become involved with others against the wishes of their partners?
It seems to me that the most important component of a "poly" relationship is the honesty. Other factors are important, but not so important as that. You may not like the people your partner is seeing; you may not even want anything to do with them! But if your partner is honest with you about seeing them, doesn't that make it "poly"?