What's the basis for this time travel "rule"?

I know Elliot's "Flynn factor" states that a non-Landry can use the pond to TT if they travel in tandem with a Landry. But what is the basis for everyone's certainty, both in-universe and in the fandom, that only Landrys can TT? Did Elliot try to TT but couldn't? As a science teacher, Elliot should know that one data point is useless in proving or disproving a theory. And we know that the pond once refused to take Alice anywhere, too.