Don't believe anything until it is confirmed, but don't throw away any information. That is the philosophy of this blog, and the reason I use it to rescue items which might otherwise be overlooked. Whether it is the paranormal, or something mundane, like an accusation of spousal infidelity, in day to day life we tend to balance the credibility of the witness with the probability of the story. If a story is really fantastic, we tend to reject it, even if the reporter would otherwise be considered reliable.
But there is a catch. Occasionally, the really fantastic happens to be part of a rare, but genuine phenomenon. If we throw away the stories every time we hear them, the data will never accumulate, and we will never discover that they form a pattern. So, even the fantastic deserves its day in court. Put it in your file. If the story is false, it will lie there, and eventually die of loneliness. But if it happens to be true, bit by bit, its relatives will drift in to keep it company.
And nowhere is this more important than with alien abductions, where high strangeness is par for the course, but there are legitimate concerns that the data is contaminated with confabulations.