The above statement is a prime example of the problem. Extraordinary claims should require good, solid evidence, just the same as the non-extraordinary claims. Anything else would be a bias against certain propositions. Doing so has little to do with skepticism or science, and everything to do with defending a belief system against evidence that contradicts it. The best stance for a scientist is one of humble openmindedness, as well as a refusal to accept or reject any proposition entirely.
All scientific knowledge is tenative.
Psi-powers and ghosts, for instance, would certainly turn science on its ear, but they have been under investigation for centuries, and I tend to the view that if something consistent and repeatable were going to turn up, it would have by now. I'll lend a more sympathetic ear. In these cases, it's more likely that there simply hasn't been enough time to accumulate evidence. I've said this elsewhere, but this seems a fairly appropriate place to repeat it. It suggests that we should be willing to believe without requiring so much strict evidence.