I had those exact stains. It's because your CYA is too high, and you don't have proper FC levels to keep the stains away. It's NOT black algae, the pool store told me the same thing. But 2 years of reading posts on this forum, I know it's not the dreaded Black Algae.
2 months after switching to BBB my stains completely disappeared and have not returned.
How did you get these test results?
You need to stop using stabilized chlorine sources like trichlor tablets and Dichlor shock. Stick with bleach/liquid chlorine. You need to drain at least half of your pool water to get your CYA in to range, if your CYA is accurate at 100. Since most tests only go up to 100, it could be higher. I would start with 1/3 of the water, at a time, refilling, recirculating, and retesting... then repeat a partial drain if necessary to get your CYA to at the very least 60.
My CYA was over 100, it took 3 partial drains to lower to 70, and then I left it there for the rest of that first summer. Then the following spring, I did another partial drain and got my CYA to 50.
Maintaining your FC levels according to the CYA chlorine chart will make them fade. But first you have to lower your CYA to a more manageable level.
Here's my stains, back in 2007, right after I found TFP and the source of my frustration:
http://www.troublefreepool.com/post5558.html#p5558