Interesting that, unprompted, they cover their tracks like this.
They seem to be "protesting too much"...
Is it sufficient to say that something that is unexplainable by science is miraculous or of supernatural origin? Maybe, but not necessarily. A truly miraculous, or supernatural influenced event, is one that transcends, or surpasses, all known phyical and natural laws.
Suppose Wallis had no life signs whatsoever, and suddenly became animate (despite an absolute lack of empricial physiological evidence of life) and coherently erudite, that'd be not only miraculous but supernatural. Throw a ball up in the air and it remains suspended at the apex of its travel. That by definition would be supernatural (and miraculous).
So then, can science categorically deny the supernatural? If one is so myopic in their perspective that the supernatural is denied, then an absolutely illogical presupposition or bias (if one is actually intellectually honest) exists, and the logical conclusion would be such person can have no hope in anything other than whatever they may epistemiologically know, or can empirically experience. By definitition, this would imply a certain sense of despairing cynicism one's world-view. That in my opinion is a hair's breadth away from nihilism.
Faith concerns itself not of those things seen, but in the unseen (and science not with the unseen but absolutely with the seen). Even so science does intimately understand "faith". There's no scientist that does not implicitely understand the meaning of faith, when, for example they board a jet aircraft and give no thought to the thousands of people who labored in the millions and millions of calculations required for the design of the aircraft (having no thought that the wings may fall off in flight). Or that whatever medication that they may ingest won't be some hideously toxic poison. That the chair that they're about to sit upon will support their weight. Such actions are done blindly, and without a second thought or rationalization.
For if faith is based on the seen, what need would there be for faith? And if there be no faith, then what can be hoped for? IF the existance of the supernatural was to be presummed, would it be illogical then to dismiss a supernatural influence of things occuring within the boundaries of physical science?. For example, could the total and spontaneous remission of "terminal" cancer be a miraclous recovery, precipitated by a supernatural force, and yet occuring entirely through some presently unknown (or even unknowable) physical process?