Science is faith based for the non-scientific. As you put it yourself, it is about trusting studies and the institutions that produced it (including whatever in them creates the incentives for p-hacking).
Comparing this to faith where from the start you cannot check anything doesn't make any sense (if you know that something is true or false it isn't faith anymore, that's the point).
I think this total lack of understanding of how the scientific process works is one of the biggest problems facing America today.
Otherwise, you could believe any PDF you can find on Google and know it to be true and representative. What if someone wrote a net to generate 10,000,000 studies on the same set of topics and scattered them throughout the Internet? Given a random study, you wouldn't know whether it's real or generated, without the "authority" aspect of a journal.
Now, whether or not the journals actually do a good job at authenticating the studies is another question. But, the principle stands that they are what we trust as consumers of science (a role which scientific researchers themselves play as well).