Opinions are always good to hear. Evidence, however, would seem to be even better. Can anyone supply a highly ranked page on a fairly generic term that does NOT relate to the overall theme of the web site where it originates? That's really all it would take to prove theming is a myth.
Theming doesn't really relate to the SEO normally discussed these days. Everyone, after all, usually talks about targeted keyword
phrases and studiously avoids going after the more generic single-word keywords. If someone types in
blue widgets california, theme isn't really an issue and I wouldn't expect the search engines to give it much weight. If someone simply types in
widgets, however, I think theming becomes more important. As a searcher, would you rather find a single page that mentioned widgets fifty or sixty times (keyword density) or would you rather find a whole web site dedicated to widgets?
I honestly don't know if the current crop of search engines takes theme into consideration or not, but I think for some generic keywords they probably should. Back in 1997-1999, Excite pretty much invented theme and used it to eliminate a lot of garbage from their SERPs. In those days, uniques were the name of the game, whether targeted or not, and it was fairly common for people to optimize one page for Michael Jordan and another for Pacman, just to get the most hits to a site that had nothing at all to do with either. I guess $35 CPMs can instigate that kind of stuff. Then, for very generic and popular terms, Excite started looking at the whole web site instead of just a page, and the SERPs improved dramatically.
As Jill said, for most sites, this really shouldn't be an issue. If your whole site is about widgets, then it's pretty much themed. In my case, however, my site was about poetry, a pretty generic term, but every poem was about something entirely different from every other poem. I had to struggle to develop a theme Excite could understand. I always ranked well on multi-word searches, where theme didn't matter, but had to really fight for the generic ones. I succeeded, but I think only because every other poetry site faced the same problem. For us, theme was hard to determine. And as well as I did, I
never was able to beat a naturally themed site like poetry dot com (I still can't bring myself to type that in a way a search engine might find it.)

Again, I don't know about today's SE's. I haven't launched a new site in two years and I've never launched one since my first that wasn't pretty naturally themed. All I really know is that theme, for some keywords, makes a lot of sense.