Thanks for the reference, never seen the article before. However, it seems to me just a big nipticking exercize, which does not disproof the point.

So to sum up the article:

- proposition (1) states the condition for a random variable to exactly follow BL (nobody denies, and that‘s also the point of my comment)
- proposition (2) is sloppy (it is)
- proposition (3) does not imply BL
- Propositions (1)+(4) bring the argument home and prove BL. The authors cannot deny it (and they don‘t) but they still submissively niptick a paragraph to warn everybody that (3) does not imply (4), as wrongly suggested sometimes.

I think the good point of the article is that (3) does not imply (4). Point taken thanks for it. Still, (1)+(4) is a completely viable proof of BL, which I honestly find completely satisfactory from a phenomenological perspective…