GrantTree is ranked pretty high against our competitors on several keywords that are important to us. This was all entirely through whitehat SEO within about a year of setting out to do it. We've just written lots of high-quality content on our blog, and then contributed genuine, original articles to other sides and got them to include a link to GrantTree or to one of our topic sub-pages (like http://granttree.co.uk/tax_credits ) in the byline. We've never bought links, nor will we ever buy links.
Now, GrantTree's context is not super-competitive like, say, Expedia or RapGenius... but we do have competitors. So competing with good, well-structured content and genuine contributions to other sites does work - at least in some contexts.
Also, I'm frequently on the receiving end of these "your blog/site/whatever is awesome and we'd love to publish a high-quality article on your blog and we'll even pay you for it" emails, and as far as I'm concerned they are spam. I never even bother replying to them.
I'll be happy if Google nails those spammy bastards to the wall - both the paymasters and the so-called bloggers.
(Note: this makes no judgement on the claim that Expedia is partaking in this)