And those independent lines of evidence are witnesses. Implausible phenomena is often simply something we haven't generally accepted as true. In order for something new to be accepted as true, its our natures to make it subject to a higher level of testimony. Witness all news scientific ideas.
For this reason, no one takes reports of UFOs and psychic phenomenta seriously.
This is false. Our military takes witnesses of UFO's seriously. It has too. It is the quality of those statements that we reject their claims. If a UFO visited NY on a regular basis and it was seen by different people each time and it occurred with regularity at some point many people would accept it as true. And many would never accept it, even if the ship landed on them.
It's a matter of judgement. There is no proof that one line of evidence is true and another false.
Absolutely. We each apply our judgment to the witness evidence that we are presented. Some of us believe there is enough witness to declare OJ guilty, some of us don't. But without witnesses, (either our own senses or the reports of others) we have nothing we can judge.
Basically I am saying that witnesses can be believed if what they are saying is believable. Science tends to file away discordant testimony until there is a theory that makes the alleged facts fit into a system of natural events.