That website really is a load of bollocks, isn't it?
"4% Glacial Acetic Acid is poured into the vessels and let to sit for 24hrs. Once the 24 hr leach is over, the acetic acid is analyzed via AA Spectroscopy for the individual metal content and then recorded."
OK, so they're trying to make out that leaving 4% acetic acid (table vinegar, dumped straight into a pan) for 24 hours yielding 7mg/l of Aluminium is a bad thing. Firstly, when was the last time you cooked in vinegar? Not "with a dash of vinegar" but "with vinegar, straight from the bottle into the pan". You've never done it, right? So that dilute acetic acid will attack aluminium is not surprising, and the answer is "don't cook in vinegar and if you do, don't leave it in the pan for 24 hours".
The water where I live has a pH of 8.1, so it's alkaline, not acid. If your water is alkaline, the idea of it attacking metal is fanciful. There are places where it's acid, albeit not very acid, with a pH down to 6. Vinegar has a pH of around 3, that is to say that it's a thousand times more acidic than the most acid drinking water (each drop of 1 in the pH scale represents an acid ten times stronger). If pH 3 will leach 7mg/l in 24 hours, ph 6 will leach 7 microgrammes/l (μg/l) in 24 hours. There are a thousand microgrammes in a milligram. Heating the water up raises the rate, but you don't cook for 24 hours, so those probably balance out. Let's throw in a fudge factor for luck and say 10 microgrammes per litre of water.
The EU limit on aluminium in drinking water is 200 μgAl/l. The water where I live already has 10, and that's a typical level. If I left every litre of water I used in an Aluminium pan for a few hours, I might, if my water was as acidic as it it conceivable, double that to 20μgAl/l. Woo-hoo: 10% of the (incredibly conservative) EU limit.
The stuff about "toxicity" of PTFE non-stick pans is similar bullshit, but it's too early to deconstruct it. Unless you're planning to buy a new non-stick pan every day and then melt a hole in it by leaving it on a gas ring for three hours, it's nonsense.