This is begging the question! You start with the assumption that assistive technologies can handle table-based layouts well, and then work backwards from the conclusion that you’re trying to prove.
It may shock or surprise you, then, to learn that in actual fact, table-based layouts caused problems for screen readers (and still do, if I am not mistaken). There are a number of other ways that websites break screen readers, and the difference today is that (1) table-based layouts are hardly necessary or even popular these days and (2) more people are suing over ADA violations for inaccessible web pages.
The screen-reader tools do not fully rely on HTML semantics, but they do need some logic to differentiate between tabular content and purely presentational <table>. The reason for this should be fairly obvious once you look at any actual web page—when you navigate tables, you want to go by columns and rows, but if you are reading a table used for layout, you probably just want to flatten it and go through the entire thing in linear order (more or less). The process can be disorienting for people with screen readers if your site is poorly designed.
Of course, if you just make assumptions and guess about how screen readers and assistive technologies work, there is a good chance that your guesses are wrong.