I work in specialized alloy steel purchasing and sales for aerospace, pressure vessel, chemical plants, etc.
Sadly, nobody / there is no regulatory body that can stop someone from buying crap steel, stamping “Stainless Steel” on it, and selling it as a water bottle. [Those orgs. do exist for industry level applications, of course.]
There are also many grades of SS, and the cheaper ones, you def wouldn’t want to make a water bottle out of. You want a bottle made out of 304L. [Or, even better, 316L stainless, but that’s unnecessary and more expensive; I’m not yet aware of any mfg that uses it.] Old people call 304L “18-8”, so you may see that stamped on bottles.
The 18 and 8 refer to Chromium and Nickel alloyed into the steel, displacing iron & carbon. They make it non-reactive. Lower grade SS will give a metallic taste to water and a weird taste to some drinks like juices, coffee, etc.
A quality SS bottle will produce no metallic taste in quality tap or mineral water. It’s completely non-reactive; you put H2O in it, and H2O comes out. Nothing is added or subtracted. If there is a metallic taste, there may be an issue with the water source, water softener, chlorine level that day if on a municipal system, etc.
Klean Kanteen uses 304L; they call it 18/8. But I’m sure there are many good brands that use quality SS; I’m not saying only KK; this is not a KK promo post. I’m strongly eyeing a Bivo, bc the KK sippy lid draws quite slowly, and makes a loud whistling sound… ok on the bike, not so cool in the cafe after! 
You can’t taste stuff that isn’t there. Something has to be there for you to taste it: When you get a “plastic-y taste” from a water bottle, that’s because there is plastic and chemicals leached from the plastic in that water, and you’re drinking it.
Yeti is quite a can of worms. They are not a gear company; they are a marketing company, a “luxury brand”. Their purpose is to charge the maximum possible for a product, and get maximum profit. You can get a cooler that holds cold equally long, weighs literally less than half, for 1/4 the price, with a lifetime warranty. I would never trust a company like that to use the best quality materials in construction; they are maximizing profit, and selling to people who just want it to say “Yeti” on it. They undoubtedly use the lowest grade steel they think they can get away with… to maximize profit.