The resistance is understandable. This pool owner is frustrated, has has a problem he doesn't understand and can't see a way to fix it. He's getting advice from the Pools Store (people who do this for a living) and from you (a friend with a clean pool) - it's very hard for most of us to doubt established authority especially when we're feeling unsure and vulnerable.
Your friend needs a reason to believe that this method (BBB) will get him to his goal. Perhaps suggesting that he read some of this forum (especially here "Dealing with Algae") would help him gain confidence.
I would also avoid attacking the pool store or the "remedies" they sold him as he likely has some personal/emotional investment in the idea that these "remedies" will help. In this case, attacking the Pools Store would be seen as an attack on him and we all defend ourselves when we feel attacked.

This is as grown-up as I get. Good luck and thanks for helping your friend.