You may be very interested in the work of Thomas Kuhn. He is a philosopher from the mid 20th century who explored precisely the concept you are looking at.
He argued that science follows a sort of pendulum like behavior. It has period where scientists refine the status quo, making small incremental updates, punctuated by periods of rapid change where existing models are swept away and new models come in.
Consider relativity as an example. For hundreds of years, Newtonian Physics was thought to be the "correct" model. Then Maxwell's equations predicted some funny things that pointed towards the need for an "Ether." The Ether was needed to maintain the status quo. Well, experiments drew doubts as to the existence of the ether, and within a relatively short period of time we developed Lorentz Transforms, then relativity itself. In the process, we gave up on precious concepts such as "simultaneity." (relativity does not have a concept of simultaneous events in a global sense. Whether two events are simultaneous or not is dependent on the observer)
In theory, non-mainsteam ideas do get tested, especially if they imply something profound. However, in practice they often go untested because it's just not worth the time and money to go test it. Very few scientists go around disproving perpetual motion machines.
Now you describe two very different things in your question. The first is results which contradict mainstream science. In this case, there is at least one experiment which can be done which is predicted to yield different results depending on if the mainstream is right, or the new idea is right. Eventually this does get tested, especially in your "open science" world.
The second thing you describe is a different viewpoint which provides a different explanation for results, even though it predicts precisely the same results. Science actually does not feel the need to concern itself with this. If theories predict the same behavior, they are "equal." This, for instance, is a major challenge for string theorists. The predictions they make which differ from the standard model require experiments well beyond our current capabilities. As far as we can tell, they are equally effective at modeling the world around us.
Another example are the quantum mechanics interpretations. The fundamental wave equations in QM are agreed upon by virtually all scientists. However, there are very different interpretations of how these wave equations should be interpreted in real life. The Copenhagen interpretation presumes a randomness that comes from collapsing waveforms. The Many Worlds Interpretation declares all observations depend not only on the observed, but also on the observer. Pilot wave theory assumes that it is possible for there to be a constantly varying wave function whose behavior depends on the position of every particle in the universe at that very moment (even those outside of your light cone)
These theories are philosophically different down to their very core. They fundamentally disagree on the nature of our universe. However, they all predict precisely the same experimental results -- results defined by the quantum wavefunction. Because they predict precisely the same results, they are permitted to coexist. They are not called "theories." Instead they are called "interpretations."
For a more current example, consider the work on the use of octonions to form a Theory of Everything. In the article, they mention that octonions are considered to be an underdog in the world of subatomic physics, but that many people find the theory intriguing.
So as for your world? We're in it.