That's not how it works when people report anecdotal accounts. If someone claims to have gone to China, is the null position, "No you didn't"? You don't go around doubting everything everyone says.
If I went to China at the minimum I'd have:
A visa
Plane or Boat tickets/ticket stubs
Passport stamps
Hotel receipt(s)
Restaurant receipts(s)
And if I make an international phone call there would be a traceable record.
As for the intermittent nature you included to try to sneak around science I have a true story for you...
For the last two years I had what the doctors called panic attacks. Finally one put me into the hospital where they ran tests, and set me up with a cardiologist. The standard stress tests, and exotic MRI's where they have you run while they've injected you with something that makes your blood glow on their screens didn't find much.
I was given a portable heart monitor which I wore for two weeks. Every time I had one of those
intermittent attacks I'd press a button on the monitor so the event was logged to be reviewed later.
Turns out I have an extra heartbeat. An extra intermittent heartbeat. When my heart skips a rhythm beat the next beat is called a Hard Start. This hard start would set off what they thought were panic attacks. Throw in a sensitivity to potassium and it was off to the races. I have medication, Licinopril, that keeps my heart from racing, and I haven't had a serious attack in ten month.
The point of the story is to get a second opinion before you write off science of any kind. That portable heart monitor I wore could be adapted to connect to a skull cap packed with sensors to monitor brain activity...in fact I'd be shocked if there isn't such a device (mine was a smart phone connected to a box the size of a smart phone).
This means that if someone claims telepathic abilities there is a way to record such activity in both the sender and receiver. That's just how it is.