No, it's not disingenious. Tables _were_ accessible and easily navigable, including by screen readers. They are also a very logical way of organizing content.

> One of the reasons we moved to XHTML, semantic markup, CSS instead of Tables... was to enable accessibility.

Again, nope. Try a design with 3-4 columns with the old CSS and see how it behaves. The order of elements in the HTML often differs from the visual order, confusing the readers.

It also breaks tab-navigation, even the https://csszengarden.com/ has the "View All Designs" button that is inaccessible.

Then add absolutely-positioned headers and other popular CSS patterns.