Its meaning is perfectly clear to anybody with any familiarity with basic logic applied to debate, or with critical thinking in general. Just like (say) 'begging the question' means assuming your conclusion, rather than its more colloquial use, and 'theory' meaning something different in the context of science than in its colloquial sense.
It's not even as obscure as those examples, it's just using 'proof' in a rather broad sense: it's up to those who make claims that they expect others to accept to provide some sort of justification for them.
It's actually quite difficult to think of a level of understanding at which it would become confusing. Those who know nothing of formal logic or critical thinking, may well think of 'proof' in a loose sense anyway, and if you know enough to see that absolute 'proof' is impossible outside of mathematics or pure logic, then one would probably know of the term anyway.
Anyway, good luck with changing the basic terminology of an entire subject because it seems so irritate you so much.....
Proof works best if it is direct or first hand proof. As an example, I have never been to England. I have no direct proof, it actually exists, based on my own fives senses doing my own exploratory experiments. All the proof I have, is based on taking the word of others, extrapolating photos and using some logic and common sense. That type of proof is not the same as actually having a first hand experience, such as landing in England and then driving and walking around the countryside. Only in that way, my five senses can fully satisfy the burden of direct proof England is real and not have to depend on second or third person accounts, that may be exaggerated, or that my imagination may extrapolate, where is should not go.
This predicament of first hand proof reminds me of the fable of the Emperor's New Clothes. In this fable, the Emperor is sold an imaginary set of clothes. At first he is skeptical, but he is told by the tailor, that only someone of refined tastes can appreciate these fine garments. The Emperor wants to appear hip and refined and he starts to see, what he is told is real, to point of denying his own eyes; 2nd hand proof is all he needs.
Others, who see the Emperor parading around naked, but with the dignity due to his fine garments, take the word of the Emperor; based on his positive enthusiasm, and they also start to see what it not there, due to the prestige of saying you can see. But eventually, a small child, using his common sense, trusts his own eyes and point out the fact the emperor is naked. Suddenly everyone realizes this first hand data, that was denied, is more important than all the second accounts of a salesman hoping to make a quick sale, by using a prestige effect.
People debate about man made global warming and climate change, but I have never seen the raw data. How many accept this premise based on a first hand account of seeing and massaging that raw data? Most of us take the word of others who do that for us, which includes the drum beat of fake news and politicians who are not even scientists. If we add the words,
consensus of science, and new Emperor's clothes appear. Consensus of opinion is not how science works. Consensus of opinion is how politics works and is used to create imaginary reality only those with refined tastes can appreciate.
Atheist require first hand experience for the phenomena called, God. They will not just take the word of others or second hand accounts. However many other things in science get a pass, with people willing to accept things they have never experienced, like dark matter and dark energy in the Lab. Spiritual people tend to have some first hand data of the divine or even metaphysical, that is satisfying to them; proof of concept of God. This is why spirituality is often personal; personal proof. If I try to share my personal proof, at best it is only second or third hand proof to you, and many feel a need to be skeptical, until they have their own first person proof.
I remember doing a development project, as a young upcoming Engineer, connected to seeing if it was possible to extrapolate an anaerobic bioreactor process, to an open basin application, where I could not fully control any of the parameters, including oxygen, pH, concentrations, heavy metals, chlorinated solvents, etc. At that time, I had no biology background nor any experience with bioreactors. A Consultant was hired to discuss the possibilities. I was told it would be impossible, since such bioreactors were very sensitive to swings in variables, and my large number of uncontrolled variables, would make it stall and not work.
The consensus agreed, but since this was my project, I had to try; spend the six months of funding. To make a long story, short, I was successful doing this in a beaker and then in an open 55 gallon drum using some soil bacteria. Then, through unique emergency circumstances, I was allowed to run million plus gallon test in an open waste nitric acid pond, which needed to be decommissioned; yesterday; EPA emergency. Nobody still believed it would work, but we had to so sometime, and this test was only supposed to buy time. However, that million gallon test became the new state of the art, for a needed treatment facility, all without any biology training. This is where I learned not to take the word of experts, but see for myself. The state of the art is a moving target and not always a stationary dogma based on second hand prestige.
