Are there any journals that pay reviewers?
It's not a myth. There are/have been some journals that pay peer reviewers. For example:


The New England Journal of Medicine used to pay $5 per review, until some reviewers complained that "if that was the price that this eminent journal placed on their opinion, the New England Journal of Medicine should seek referees elsewhere"
The Lancet reportedly pays for peer review "sometimes"
Reviewers for journals published by the American Economic Association earn $100 for each "timely" review.
Zentralblatt MATH (zbMATH) pays 2.56 EUR per review, although this is for post-publication reviews that are then published.
The Journal of Medical Internet Research offers "a review model in which selected peer reviewers may be paid to deliver high-quality and speedy peer-review reports" (if authors pay an extra fee for the fast-track option)
The Arabian Journal for Science and Engineering has offered an honorarium of $100 for each "timely" review
Drugs in Context pays its peer reviewers an honorarium of unspecified amount, supposedly "to motivate rigorous peer review"
The International Institute for Science, Technology and Education (which is on Beall's list of allegedly predatory open-access journals and publishers) pays reviewers for its journals $60-$100 per review


Whether the reviewer being paid, has more obligations to provide thorough in depth review is true or not is entirely uncertain, though.