Even in your definitions, Natural Philosophy (2) is more properly known as Physics...
I think Ashton is saying that there are many things that science can't explain. I think Peter is saying that a purported scientific proposition that cannot present an explanation that is supported by evidence is not, in fact, a scientific proposition. "It's bollocks."
In fact, what Peter said was that everything 'paranormal' has been 'found' to be either fraud or chance.
Now, I don't know about this instance of trying to fit 'paranormal' phenomena into a scientific framework, myself. But if he really meant "that a purported scientific proposition that cannot present an explanation that is supported by evidence is not, in fact, a scientific proposition "It's bollocks."" in general, he would HAVE to reject both 'dark energy' and string theory, and say that they are 'bollocks'.