Extraordinary claims require extraordinary evidence. The burden should be on Robert to prove he's running the whole way. And clearly he's not. Now that this stuff is surfacing, he will likely bail, start running legit (and miss the record), or change his route so he doesn't get caught. Don't wait for him to fess up; it'll never happen. That twat-face dane still claims he ran that 202 miles even though he slept in the RV that drove him along the course. Same thing here, only Robert is doing it 15 times in a row.
You're absolutely g-dd--mned right. Extraordinary claims require extraordinary evidence. These days, it's really easy to provide irrefutable proof.
Here's a hypothetical. If I wanted to set a record for the coast to coast run and I was convinced that cheating was the way to do it, I would take advantage of the long desert stretches in the first 25% of my crossing and that's when I'd cheat: at night, in the desert. That is the ONLY time I would cheat. That would put me ahead of schedule, and by being ahead of schedule I would guarantee myself added attention.
This is purely a hypothetical. But that's how I would do it.
On the other hand, if I wanted to set a legitimate record, I would use available video technologies and create one long time-stamped video file of my run.