Back in the 20th Century there was a movement called Neo-Orthodoxy. It was spearheaded by such theologians as Karl Barth, Emil Brunner, and Rudolph Bultmann.
Beginning as a reaction against liberal Protestantism, one of its key tenets was that historical investigation was not to be relied upon for to provide verification for scriptural historical claims. Instead, Neo-Orthodoxy began with human experience for doing theology.
The reason I bring this up is that some elements of Roman Catholicism, and the so-called "Reformed Catholicism" seem very much, if unintentionally, influenced at this point.
In reading several conversations between Evangelicals and the RCs and "rCs", I have noted that the claim is made that the standard method of biblical interpretation, known as the Grammatical-Historical Method, is invalid as there is no sound epistemological foundation for it (epistemology deals with the question of how we know things). This, it seems to me, is not unlike the claim that the Neo-orthodox made.
Another similarity lies in that RCs and rCs seem to claim that the individual must reckon first with the epistemological issue and then build a theology. This beginning with the individual seems again to hearken to the Neo-Orthodox notion.
(On a side note, the emphasis on the individual is ironic since both RCs and rCs seem to decry the "every individual an interpretational island" idea.)
But if this seeming connection to Neo-Orthodoxy is true, then the thinking of the RCs and rCs would share the same weaknesses, such as it being essentially fideistic, as it insulates itself from any kind of verifiability or falsibility. That makes sense as neither RCs nor rCs have actually put forward a positive case for their position. Perhaps it is because, under the influence of Neo-orthodox-style thinking, they don't see the point of such evidence. It is also vulnerable because it makes a claim about history that is inconsistently applied (in that they accept the historicity of the resurrection on usual historical proof grounds without the issue of epistemology arising) and actually essentially skeptical, meaning it is at bottom negative, and can therefore make no real positive contribution to theological method or hermeneutics.
Now in saying this I am making no claim to being a master of Neo-Orthodox thought; these are at best impressions garnered from a few years of seminary and some random book reading from Neo-0rthodox authors. Please take this post for what it is; a suggestion, and perhaps a starting point for discussion, thought, and debate.