I've never heard that and none of the links provided in the comments so far justify your claim. It is a pretty extreme assertion and you provided no links justifying it either.
I can see this rapidly turning into an urban myth, whispered wild eyed at 3am over ramen noodles as founders try and figure out a price for their product.
Not quite - price discrimination is finding a way to take people with more money, and charge them more money. The challenge is, that prices people with less money out of the market - so price discrimination is about finding ways to justify cutting prices for some people while charging more to people who can afford more.
Examples: Student discounts, senior citizen discounts, kid's meals, and matinee prices at movie theaters are all price discrimation. A/B testing prices is... just A/B testing prices.
Though, the wise A/B price-tester does so by offering two different sales - one discounted product, and one more discounted product. This seems to minimize backlash - finding someone else got a better discount doesn't bother people as much as finding out they paid a higher price.
I'm not claiming to know this of all jurisdictions, there may be specific circumstances in which this does not hold, but these are the exceptions.
You're thinking about laws around hiring. I can't charge you double to buy a VCR in my store because I don't like your face.
You're thinking that just because people don't do it, it must be illegal. The idea of "one price for identical items" is a pretty recent invention, dating back to the rise of department stores (Woolworth's, Macy's, Sears) at the turn of the 20th century. It's for economic reasons, not legal ones. They found that it was cheaper to forego the extra revenue than it was to hire all the salespeople needed to negotiate each individual purchase. Charge less and make it up in volume. It also has the advantage of fairness and simplicity, which customers tend to like.
I think he's right though that there needs to be some linkage to "what you can and can't do, legally".