Using the W3 online validator for testing, you can certainly create an invalid, but semantic web page -- as easily as you can create a valid page with meaningless markup.
However, I believe validation and semantics are one-and-the-same (or rather, that they should be). Automatic validation is the limitation. A computer has little idea of the semantic meaning your documents should represent and is unable to verify you have followed the W3 specs in this regard. Despite being reasonably painful to trawl through, the W3 specs often suggest intended semantic usage.
In this way, the W3 validators are similar to the accessibility validators, like Cynthia Says and WebXACT (Bobby) -- at some point they require manual (human) validation to be accurate.
I'm not saying there aren't a lot of 'grey' areas -- there are. I suspect this is why less emphasis is placed on manual validation of semantics.
Still, I wouldn't jump on anyone who tries to describe something in the 'simplest' way possible ... simple statements are always prone to being general and, of course, simplistic. Let's not even go into the fact that a valid web page isn't required to use CSS at all. ;-)
I don't think they're the same things. A table-based layout can be made up of valid HTML and not be particularly semantic.
I also don't agree that the W3C validators should be viewed like accessibility validators. The W3C validators are checking HTML & CSS to ensure the code is interpreted properly by machines. If the code has no errors in it, then a page should be viewed as being 'code' valid. They're not designed to say anything about the content and I don't think they should either.
Of course, just because a page has valid code doesn't mean it is semantic or well-structured. Which is why I don't think validation and semantics should be the same thing. Validation is just one part of the overall process and I think a distinction should be made so that web authors have to do more than just be able to display a validation badge on their site to think they've done enough.
@John (Tyssen): I don't disagree with you. Straight off the bat I mentioned you can create a valid page with meaningless markup (eg. not semantic). Perhaps I wasn't very clear?
I tend to think of validation and semantics as the same thing because that's how I describe 'professionalism' ... (or at least two important ingredients of it -- I don't intend any offence) ... Why do one and not the other? They compliment each other perfectly -- imo. So, I'm saying they're different but also the same (I love contradicting myself). ;-)
Do we need a 'professionalism validator'? (Did I just hear a chorus of groans? teehee!) I think it could be useful ... but, as I mentioned before, there are a lot of grey areas and it would be difficult (if not impossible) to implement without human interaction (and even then humans are bound to disagree).
Of course, the XHTML and CSS validators are currently only code-checkers. I should have been more specific: I was thinking hypothetically -- in the context of checking usage of semantics, as implied by the W3 specs. I stand by my idea though, if it were at all possible, I think it would be useful to include semantic-oriented suggestions within the validators. These suggestions wouldn't affect the outcome of the code-validity. If anything at all they'd be warnings -- not errors.
Having said all that, I especially agree with your last point about 'thinking beyond the badge'.
Mind you a truly a semantic page, does not take into account the stateless nature of the web. And assumes association with its parent, and siblings. Hence that's really subjective.