People "lose faith" in their governments. It doesn't mean they stop believing their governments are real. I've "lost faith" in friends before. It doesn't mean I started doubting my friends existence.
There is a difference with how people's mind deal with physical reality and remarkable proof of God and faith in him, there is also a difference between correct thinking and erroneous thinking. You have correctly pointed out correct thinking but your examples only show how people should deal with reality logically but you failed to show that when people do not like reality they try to fool themselves into believing that reality does not exist so they do not have to deal with it, for example, alcohol. suicide, denial, etc.There are more examples and it is a long topic to discuss but I think that it is sufficient to give a couple examples that show that when some people loose faith in reality they sometimes do not think correctly especially when reality hurts very much and they have to deal with it and the only way to cope with such pain is to believe that reality does not exists even though in the back of their minds they know it. The examples that I gave of people that know God is real but loose faith in him and forget about him sometimes come to their senses and realize that they failed to look at reality correctly.
Same as when someone reads an article or a post and does not read between the lines or or see what the author is inferring, people can be looking at at something real all of their lives and do not knowthat it is there until they change their perspective and realize the obvious or until it strikes them over the head and then they see. You have heard the expression: "I see!" said the blind man.
"It is comical." -Marvin Shiimer to hear people demand proof of God from other people. As if God was some puny thing unable to give every individual a special personal answer -just for them.
There is a problem posting I posted other information and try editing some of my choice of words that afeect meaning of some of my and cannot post through.