RE: All facts are subjective

Strictly speaking a “proof” is a process with a system of logic whereby one demonstrates that if certain assumptions are accepted or found to be true, then some conclusion necessarily, logically follows. Facts are never proven in this strict sense of the word. The tests for facts are empirically, a question of preponderance of evidence supporting or disconfirming. Sloppily and popularly this is often called “proof”, but it is really a very different thing. 

Facts “continually ‘proved’ and… not ‘disproved'” means merely that people have judged the evidence available and find the fact supported by the evidence. That doesn’t mean that the fact is right/true in any objective sense. What it means is there is intersubjective agreement about its validity as a model. Still knowledge. Still existing in the minds of some set of knowers, without whom it would not exist. Still subjective.