If the voltage does not drop when using 2x3.7v bats it won't drop using 2x3.0v bats. This isn't an opinion, it's the simple application of Ohm's law. That test was absolutely valid.
That is not a proper application of Ohm's law. You are assuming that we are testing a single physical component (a resister), but we are talking about a voltage regulator circuit that was designed to output 5V when supplied with 6V and 7.4V when supplied with 7.4V.
The video shows the Xhaler working as advertised.