By your reading, no theory can ever be known to be well founded, as there is always the possibility of another discovery finding phenomena that aren't explained by the theory. I believe that most people would view science (in the wide sense, not limited only to disciplines that apply the scientific method) as a continuous process of abstraction and refinement. Newtonian mechanics is pretty accurate if you limit yourself to objects of a certain size and a certain speed, a limitation which is reasonable considering those are the sides and speeds we encounter most often in our senses.