What would you do if an alien came to you and took you for a spin in his "saucer"? You would have sufficient evidence for YOU to believe in such things. But it still wouldn't be science. There is a certain consensus involved with evidence that can be called "scientific". If you were going to be completely objective you would have to view yourself as having experienced a temporary condition of insanity. In such a case you would be wise to go to your doctor and get an MRI.
You actually raised the most essential issue!
We, as individuals, don't require consensus to convince us of our own experience. That is group-think and it is dangerous (as Nazi Germany reveals). Our individual personal experiences inform US with advantage.
It is only when the group at large is presented with choices which involve your input that skeptical inquiry is useful for the group.
Objectivity means "the same for all". Personal experience can never be objective.
"Others" can only extract from personal testimonials the particulars and not the emotions, the impact and the resonances. Religion most errs in accepting testimonials lock, stock and barrel by assuming the emotional "truth" while ignoring the untestable nature of the data which "caused" the emotions.
I believe my experiences as they pertain to me. When I start extrapolating beyond what I suffer I'm on shaky ground. A thirsty man in the desert actually "sees" water on the horizon. But, the group can only learn from his experience when it ends in death due to buying in to a mirage. You see?