We also suggest you link to other pages of your site using absolute, rather than relative, links with the version of the domain you want to be indexed under. For instance, from your home page, rather than link to products.html, link to http://www.example.com/products.html . And whenever possible, make sure that other sites are linking to you using the version of the domain name that you prefer
This seems to me a classic example of taking things out of context. If you read the entire article you can see that Ms. Fox is talking about a specific case where your site can be accessed by more then one domain name (e.g. http://www.domain.com and http://domain.com).
There is nothing google ever wrote that i could find that say that absolute URLs are better if your site is only accessed by one domain name.
There is one exception i can think of: if your domain is "coolstuff.com" for example and you do use absolute URLs, then the word "coolstuff" will appear in your pages alot. This might be something that may boost your ranking with regards the the word "coolstuff". But this is just a guess.
More reading: Google Canonicalization Problems? - Crawling, indexing, and ranking | Google Groups
Please note: this is my personal opinion. I've had at least two SEO experts that claim that absolute URLs will give better performance on google ranking. Since I'm strong-headed I will hold to my opinion until I'll be proven (with numbers) otherwise. Feel free to comment with supporting or conflicting opinions and data.