The issue is that synergism, while a characteristic of Arminianism, is not Arminianism itself. But you do bring out another problem with the debate within the SBC. Terms are being loosely used and poorly redefined (synergism, to varying degrees, is indeed present in many SBC churches but Arminianism is contrary to SBC doctrine).
This problem goes beyond the SBC also (probably everything we are dealing with exceeds SBC boundaries). I've read many articles about the Arminianism of Anabaptist theology. Don't miss that!!! Anabaptist theology, which rejects the view of Atonement both Calvinism and Arminianism hinges upon (the Penal Substitution John Calvin articulated and John Wesley strongly defended), is being called "Arminian" because of its synergistic nature. Likewise we see just about any type of soteriological determinism referred to as "Calvinism".
Another interesting error people make in labeling others is to call Open Theism "Arminian". I think that it may be of that trajectory (just as Arminianism is of Calvinistic trajectory), and I believe both share a common understanding of the mode of Divine Knowledge (a pre-knowledge of events). But it is pretty lazy to use "Arminianism" and "Open Theology" interchangeably.
This vagueness is a type of laziness (perhaps apathy...or misunderstanding) that is not helpful at all.