Article submissions - get discounted because of dup content Directory submissions, that's like few hundred links max, most of them will not count PR's to newspapers? Buying links... are you saying they bought tens of thousands of links?
Not sure about "authority" links. However, you can easily buy sitewide links that will get indexed as tens of thousands of backlinks.
Providing useful tools that your customer needs is a good strategy to get inbound links. One good example is the text-links calculator that text-link-ads.com implements
There are a way to get more of backlinks than thounad - social networks. They are really can help to get more links. Just provide good content for page to which you'll lay out link, it must contain interesting infromation to provide a great social reaction - and you will receive links from great nubmer of links from numerous of users. This is a report about one submission tool mavericksocializer.com/free-report.html (copy-paste url in browser) There are good article about social bookmarking dlib.org/dlib/april05/hammond/04hammond.html(copy-paste url in browser) Both links are good.
How old is the website? I think that would make a difference. If a site is say 10 years old, I could see how they could have easily acquired that many ibls.
How do myspace sites have thousands of links to them? How does DP have (some crazy amount) of links, how does CNN get so many links? How does statcounter.com have so many links You need to do something different and stand out..do something useful...give people something free (and put your link there like myspace sites....)...