It has nothing to do with the amount of markup used though that is a bonus for tableless designs. It is all about semantics i.e. using the right tag for the content. For example, if you have a paragraph of text put it in a <p>, if you have a numbered list put it in a <ol>. Tables therefore should only be used for tabular data such as the main sections of the index and viewforum pages and be correctly marked up. Divs have no semantic value at all so they are safe to use for layout; they are invisible in text only view and are ignored by screen readers.
It's also about flexibility. If you use tables for layout then you are stuck with a grid. If you use tableless design then you can shift everything around with css without ever having to touch the markup (in theory). You just try overlapping stuff that is in a table cell. For example, take the board statistics box on the index page. If that used a two column table then you would be stuck with one bunch of stuff on the left and another on the right. With a tabless layout I can change one item in the stylesheet and stack things on top of one another instead.
I wouldn't worry about Netscape, the big debate now amongst developers is whether to dump support for IE5. PunBB will never work in very old browsers for the simple reason they don't understand css. In the end its just a decision whether you want to support the maximum possible browsers or whether to look to the future and be ready for the time when the the likes of NS6 and IE5 are just distant memories.