No, actually they don't. The same criteria apply to all science phenomena. This phrase originated among the career skeptics to put down science-based research into paranormal phenomena. It has zip to do with legitimate science.
"But I’m more than willing to be convinced if that evidence is supplied.
One well-done experiment (or series of experiments) and one replication of those experiments at a different lab are all that is necessary.
Disagree. Displacing a well-grounded scientific consensus with a totally new explanation of observed phenomena requires, and IMO should require, more solid evidence than a claim with less evidence already in existence on the other side.
What a coincidence. Cold fusion also has zip to do with legitimate science.