I'll choose the example of quantum mechanics to try to explain how ideas are established in science.
Think of a guy called PhotonicBoom who has a theory which is, like any other theory in physics, highly mathematically dependent. Lets call it Quantum Mechanics (QM). If the theory is mathematical, it has the advantage of relying on reason. You can use this to make predictions. In a hand-wavy way, predictions can be made by extrapolating the theory, and devising a way to test if those predictions are true. If the prediction is shown not to occur in nature, then you throw the theory away and start from scratch, it has been shown to be wrong.
In our case of QM, people came up with the hypothesis that, for example, energy levels are quantised. They formulated the mathematics of the theory and then 'extrapolated' the theory to make predictions. And QM did predict a wide variety of phenomena, most of them extremely bizarre.
But QM has survived every single test it has been thrown at it. This hints that we have the correct theory, whether we like it or not.
And now follows the obvious step. Making sense of QM. How do we make sense of extremely bizarre phenomena like entanglement, tunneling, superposition, state collapse etc? Well there is one easy and obvious step. We try to link concepts that we do know of, concepts that we grew up with and have hard-wired in our brains as "Status: Makes sense", even though these concepts have no reason to be more 'sensible' than other concepts.
And this is what we have done. We attached classical concepts to quantum mechanical ones, i.e think of spin, tunneling, wave-particle duality, state collapse, entanglement as an active link. All these concepts are hand-wavy, they are technically not 100% precise to what is really happening. But, they make sense, and also they are very useful at explaining what is going on at most, but not all, situations.
In your particular examples, we have attached the notion of a particle to what a tunneling microscope interacts with, but more precisely the microscope is actually detecting discrete jumps between potentials. But the atom model is an equally valid description of what is going on since these electrostatic potentials are what we call the atom in the first place! How we represent them on an image is arbitrary and is mainly used to give us intuition, it does not necessarily represent the truth.
Then you mention quarks and the Higgs. We might not be 100% sure that quarks or the Higgs exists but hey, these models have made predictions. These predictions have been experimentally verified. So what reason do we have not to believe in the existence of these particles? Just because we don't describe them with their exact technically correct terminology (that would be extremely painful, for example for the Higgs discovery: "We have successfully detected traces of the quantum excitation of the complex quantum scalar field with non-zero expectation value!") doesn't mean that the words 'particle', 'quark', or 'Higgs' are not enough to transmit the message. The point of this paragraph I guess is that the physics is there, whether we attach them some common sense term or not.
So to finish off, no QM is true (if its a precise theory or not is completely irrelevant) and has no dependence what so ever on history or the language we use to describe it. What would have been different are the interpretations, but those are just a construct to reduce the terminology to more "everyday common sense stuff" for communication reasons. You should be careful not to attach a very literal meaning to these interpretations, and definitely not to think of them as a definite truth. Things can be described in many different ways!
I hope I have been coherent in my long answer!