Of course avoiding tables doesn't automatically make things accessible. It makes it possible to be accessible.
Accessibility is tricky. For instance, one of the largest things that HTML tables break is the linear flow of the page. For people using screen readers or text-only browsers it becomes far, far more difficult to understand the content of a page.
CSS tables can be applied with consideration only against the hierarchal structure of the page allowing you to write pages that are accessibly legible yet stylish.
That is unless you want to make whole new versions of your site for any number of accessibility domains: modern browsers, IE 6-, blind people, lynx, mobile browsers, mobile safari, colorblind people, &c. Good luck with SEO on all of those, too.
Real, successful sites do make multiple versions for mobile and regular browsing. If neither of those work for you then you are a rounding error on a rounding error that's ignored.
Regardless, use of tables means absolutely jack * as to whether real life sites are "accessible." Lots of this anti-table stuff makes sites less accessible to regular users.
Regular and mobile browsing is one major exception. It's also generally not the trend that I'm referring to. A good site probably does make up to three versions for screen, mobile, and print views. Some sites might even, serendipitously, make out by just changing the stylesheet.
Avoiding table based layouts is not the definition of accessibility and I never implied that. They are frequently a symptom of poor accessibility, however, and then they almost always obscure the intended hierarchy of a page which defeats accessibility for text based browsers and screen readers and messes with SEO.
Accessibility is tricky. For instance, one of the largest things that HTML tables break is the linear flow of the page. For people using screen readers or text-only browsers it becomes far, far more difficult to understand the content of a page.
CSS tables can be applied with consideration only against the hierarchal structure of the page allowing you to write pages that are accessibly legible yet stylish.
That is unless you want to make whole new versions of your site for any number of accessibility domains: modern browsers, IE 6-, blind people, lynx, mobile browsers, mobile safari, colorblind people, &c. Good luck with SEO on all of those, too.