I think you're misunderstanding the use of the word "accessible" here. Scientific proof must be able to be observed with no conditions of faith. Just because someone accepts a sunrise as proof of god doesn't mean it is proof. It just means that person has lowered their standards for proof.
No I am not, I am pointing out that repeatability is not a criteria of science. despite the massive amount of ignorance that permeates this board on the subject. It is nice that things are repeatable because it makes it easier for other people to double check the work, but some things are not, by their very nature, repeatable. For example, Shoemaker-Levy gave us a lot of data about the makeup of both comets and the atmosphere of Jupiter, but no one is demanding that the data be repeated with another identical comet before the data can be used to argue their favorite conclusion.
Which brings me to another point, stop using scientific as an adjective to make it seem like there are different types of proof/facts, it just emphasizes your ignorance. All evidence is of the same value, what matters is how you analyze it to draw conclusions. There is nothing scientific about data because data is not a process, and the scientific method is a way of analyzing that data.
Also, there is nothing in the scientific method that prohibits you from approaching the data without a belief set, or faith, as long as you are willing to accept the possibility that your beliefs are wrong. Quite honestly, it would be impossible for a human to approach anything without expecting to find something. You cannot analyze blood without the faith that it is composed of red cells, white cells, platelets, and plasma. That is what you are looking for when you start,so it is perfectly acceptable, and part of the scientific method, to have faith that they will be there. The big news would be if they weren't.
The problem here is not the people who have faith, it is the people who don't understand faith. Or science.