Supernatural vs. Scientifically Unproven

I was just wondering what people's views on this were. Is supernatural a possible synonym for scientifically unproven? People have said that bigfoot, UFO's and the like are supernatural, but so were giant squids and the northern lights before science proved their existence was real. In the case of squids there wasn't a lot of physical evidence (at least no more than there is for bigfoot or UFO's) until recently. So, is it really acceptable to flat out reject something based on it being 'supernatural'? I say this, because it seems as though there is some close-mindedness out of the materialist camp. Since things like souls or God can't be proven by science (yet) then the possibility is rejected. This seems like the similar arguement that is frequently used against Christians (or any other religion for that matter). Basically everything is molded around a preconceived set of values for how the world operates. In the case of Christians people try to mold science around the Flood, etc. and in the case of materialist there can be no such thing as OBE's, NDE's, or ESP. So, does supernaturalism have to be reduced as phenoma that is 'miraculous' or can it simply be in defiance of certain principles we currently know about physics?