Your numbers are backwards. The 6.5 is the uvi meter. 6.2 is the uv flux.
The problem with measuring UV flux is that the same number can mean completely different things from different sources. when measuring the sun, you know what to expect. The problem comes when using it on lamps as different lamps produce ratios that are different than the sun does. That's why francis has mentioned that a lamp that was only producing 50 mW uv was causing severe skin and eye issues. It wasnt until they realized that the ratio of short wavelength in that 50 mW was much higher than other bulbs or even the sun. So while being exposed to the sun at even 400 mW wasnt causing issues, 50mW of this specific lamp was. If your meter only can measure mW like the 6.2 does, you really dont know how much of that is actually shorter more intense wavelengths unless you rely on a chart. And if that's the case and you are going to rely on a chart anyways, there really is no point of getting the meter.
The 6.5 and the UVI reading specifically targets the wavelength range that is responsible for causing sunburns and d3 synthesis. That's why most companies/zoos/experts are using UVI now, as mW from one source can be drastically different than the same mW from another.
Hence the 6.5 being the preferred meter.
It's definitely not pseudoscience.
-Brandon