I think you can differentiate between people who say that about a skill, and people who say it about a concept.

Consider driving: I recall driving being a System 2 activity for at least a year while I was learning. It was certainly stressful enough to induce tears on a regular basis (give me a pass, I was a teenager). Slowly, driving under normal conditions became integrated into System 1, and now I don't feel like crying when I have to change lanes. Sufficient practice of any skill can turn it into a System 1 activity.

Currently, programming is a System 2 activity for me. My husband, however, has more than a decade of experience programming. When he helps debug my code, he doesn't painstakingly go over every line, first thing. He glances, skims, says "This doesn't look right..." and then uses a combination of instinct and experience to find my error. I can't imagine being a professional programmer until it's a System 1 activity at least half of the time.

So: the difference between saying "System 1 is integral to my profession and execution of a skill," and "System 1 is all the evidence I need for the existence of a deity" is very large. In the first case, we can take the statement as evidence, appropriately weighted against the speakers track record with that skill, that System 1 has been beneficial. In the second case, people are saying the equivalent of "My instinct = God, and that's the only test I need!" The weight that bears in your Bayesian calculation should be nothing, or almost nothing, because there is no way to develop a God-detecting skill and integrate it into System 1.