Planet13 - 10:39 pm on Feb 21, 2012 (gmt 0)
Is it coming from their own databases etc (like they would have their own bots crawling the Internet and indexing that information in the same way the search engines do)?
I don't know about ALL the companies you mentioned, but SEOMajestic and SEOMoz do have their own crawlers.
I prefer majestic over SEOMoz, but others prefer the other way around. Neither of them is perfect.
Linkassist used to use yahoo site explorer, but now that they have merged, I don't know what they use.
Hope this helps.