Not exactly. If they aren't confirmable by the methods of science they aren't confirmable in any way that is convincing. All kinds of things are asserted by charlatans -- ESP, precognition, remote viewing -- you name it. If the phenomenon vanishes under scrutiny, it might as well be rubbish, because no one who is not motivated by wishful thinking will allow it to affect the major decisions in life.
Oh, come on.
It is human reason that confirms that the scientific method is reliable. If nothing were convincing to a reasonable mind before science, no reasonable mind would have ever accepted science.
Ah, but if I've understood William James correctly, the phenomenon in question does not vanish under scrutiny. Science can "see it"; it just can't "explain" it. It has no method for explaining the observed mental phenomena of, for instance, intention, attention, and will. These are not involved with processing data of sense perception coming in from the external world, but are activities that are purely internal to the mind. And they can generate phenomenal effects in the exteral world. In other words, their contents do not arise from external stimulation, but from free selections and combinations of data that can be accessed from memory, which can then be additionally "processed" in new and different combinations, in newly meaningful ways.
There is no evidence to support the theory that this is "just" the brain doing all this. The brain facilitates, but is not the driver, of processes such as these. IOW, they are not epiphenomena of brain neural activity. Moreoever, as noted, since they can lead to external empirical effects, we can't call them epiphenomena; for part of the definition of an epiphenomenon is that it is something that cannot cause anything to happen.