Broken link building
Your confusion re broken link building is well founded because you are misunderstanding it. BLB is the practice of identifying sites that have a broken link then approaching the webmaster to let them know about it and asking them to replace the non-existent URL with your URL.
The part I disagree with is "randomised". It if were random, then I would get different results each time I looked.
I agree. Randomised is not an accurate description. The backlink search has always shown a sampling. Perhaps "sampling" is a more accurate word than randomised.
Here is the history: Google used to show just links from pages PR 4 and up. But that led to the belief there was something wrong with pages less than PR 4, causing people to not link to them. This mistaken assumption continues, although most SEOs don't know why PR 4 is the threshold. Legendary Internet marketer, Dave Naylor, (http://www.davidnaylor.co.uk/) approached Matt Cutts during PubCon London (2005) with the problem and suggested a more useful "sampling" of backlinks that included sites from a broader range of PageRank levels. Matt thought it was a good idea and brought it back to the engineers at Google.
As far as Title Tags playing a role, Google has consistently encouraged using title tags that accurately described the topic of the page. I know from experience that an accurate title tag will help rank a page better than a title tag that is optimized for a high traffic keyword phrase. There's a difference. A high traffic keyword phrase is not always what the page is about.
For example, I was on a site review panel at PubCon and we were reviewing a site about example advice. The site owner's complaint was that he couldn't rank for higher traffic phrase. So I asked him, is your site about higher traffic phrase or is it about example advice. His answer was that it was about example advice. Having spidered his entire site and reviewed his title tags and the top level content of his site, I agreed and pointed out that that is what he should be trying to rank for, not the phrase with more keyword query traffic. His site was not about higher traffic phrase. His site was suffering from poor title tag choices and well, he knew enough SEO to shoot himself in the foot.
That was a classic case of SEO as a way to trick the search engines. SEO is about optimizing what you have, making your site topic crystal clear by making the right choices, such as page speed, good topic organization and site architecture. Trick SEO is about trying to convince the search engines that the topic is about something that it really isn't about. Trick SEO is a symptom of a failure to understand what optimizing is really about.