Right, I think I agree with you.
Re science - I am using it in a generic sense. In the sense that I think most people use it, where they will often contrast it to religion.
But!!!
Do you not think this applies to people who hold that science is not like religion. Another comment mentions 'falsifiability and testability' which I think this is key.
The key point I would add is that no one (NO ONE) is testing or falsifying the 'science' information they receive! When they look at science papers online, they may as well be sitting on a pew! Especially when you consider the Replication crisis. (https://en.wikipedia.org/wiki/Replication_crisis)
Knowledge and knowing is NOT a group activity. It occurs in an individual's brain. You can know if you have personally verified, or you can assume/believe/hypothesise. Most people who would argue for the primacy of science over religion, are actually in a state of belief - their knowledge is theoretical, hypothetical.
The scientific method only has any meaning when it is applied personally, rather than assumed.