I think the issue is even more basic than that. You can use the (X)HTML validation links, and it sounds like those are fine. You can't use the CSS validation links because your site doesn't validate. You're stuck with a framework with bad CSS, and visitors are going to have to deal with that. As long as you don't have the valid CSS link you should be fine. I don't think you have any issues at all. And realistically if you're trying to make your site "look" valid to the validation software even though its not, you have a much more basic problem, honesty and usability. Your visitors are going to be affected by the issues of bad CSS, it would be inappropriate to tell them your site's CSS is valid. It doesn't matter if it's one particular stylesheet, that's still an integral component of your website's CSS. In my experience you don't want to establish the expectation if you can't deliver the goods. That's not a bad thing. If you, your visitors, and / or your clients want to take advantage of the benefits of the framework, then bad CSS is one of the tradeoffs that goes with that. It doesn't mean anyone is doing a bad job, it's the evaluation process you go through with any 3rd party software / component / etc. It's just important to be honest about what things do and wahat they don't. It's all about managing expectations. And that's the big reason you wouldn't want a valid CSS logo on the site.
That being said, IMO, I hate the validation logos. I find the entire idea tacky and never recommend using them.