To address this, I believe we need extra precision that’s usually omitted from discussion and analysis.
P is what we might call an “abstract” idea addressing an “abstract” problem. This may not be the best word but I’ve used it before: Curiosity – Human Problems and Abstract Problems
P is not a decision for a human to make.
An abstract problem is “Are there aliens?” which is the kind of problem that P is responding to. In some sense, the right answer to that is “I don’t know”; it’s not a solved problem. It may not be solved for centuries.
The problems we deal with in our lives are a bit different. They are more like “Should I believe there are aliens?” or “What should I believe about the potential existence of aliens?”
To address problems like those, you use statements similar to but different than P. E.g. you might say “The best conclusion to reach today is that it’s plausible that aliens exist.” This statement contains P as a sub-statement. It could also be written as “The best conclusion to reach today is P”.
This gets into the realm of human action and human decision making. It’s still a fairly abstract type of decision (what to believe). Sometimes what we care about is more concrete: what physical or external action to take. We often are trying to decide on a belief in order to make some decision involving the external world. Like I might be deciding whether or not to build and launch a space probe to look for aliens. Or I might try to form a belief about whether a particular product is counterfeit specifically in order to inform my immediate decision of whether to buy it, not just as an intellectual curiosity. Or I might try to form a belief about whether there is a McDonalds two blocks to the right in order to decide which direction to walk.
Looking at this from another angle, we have to be clearer about the goal. You specified P but didn’t actually specify the goal. Since there is no goal, CF says it’s technically impossible to criticize P except by pointing out the lack of goal (or by inferring or assuming some unstated goal). Adding context about human lives, decisions and actions is a way to think about the goal. For example, the goal might be to reliably arrive at McDonalds, in which case an arbitrary assertion isn’t good enough even though it could be true. To reliably arrive at McDonalds, we’ll want to navigate using arguments, evidence, or more broadly a good methodology. Similarly, any issue related to what I should believe can be interpreted as having a goal about using rational methodology.
The word “plausible” makes P less abstract than it could be. Plausible brings up human mental states in a way that Q = “Aliens exist.” doesn’t. This suggests the goal of P is about figuring out the right mental state to have about Q. If that’s the goal, then methodology and rationality are involved, because the right mental state to have is the one you reach using rational methodology, not whichever one is true (you have no direct access to omniscient truth. if you believe X for no reason, and later everyone agrees X is true, and we assume for discussion that X is true, it still wasn’t the right thing to do to believe X in the past for no reason; you just got lucky).
BTW, “plausible” isn’t how CF typically describes ideas, which I think makes this a bit more confusing.
So the short answer is you skipped the step of explicitly stating the goal and the longer answer involves goals related to rational action, belief and problems people face in their lives, not just abstract truth. That makes criticisms about reasoning, methodology and sources relevant to the goal. For issues that are purely about abstract truth, the right answer tends to be “I don’t know”, or perhaps not to answer since it’s not actually related to your life. CF, like all fallibilist epistemologies, does not definitively prove statements true or false; it merely helps guide humans in their lives, thinking and decision making. All CF refutations are “tentative” and “fallible” (open to potential revision in the future) just like CR refutations.
Also, to avoid potential confusion: I used singular “goal” because you can conjoin goals together, so pluralizing it or not doesn’t really matter.