How else is a tool going to search for all backlinks to a site but by using a search engine? A search engine, like Google (or Bing) has the resources and power to index millions and billions of webpages.
Unless a particular tool has been indexing their own web engine, the tool will be forced to use a preexisting index, most likely Google.
If that is the case, then they will be limited to what a search engine is willing to reveal about their indexing methods, which will not me much. If, let's say Google, were to give you an accurate measure of all backlinks to your site, then they'd be compromising the integrity of their algorhythm(s).
The very basic answer to the OP is that Google values the other site as more authoritative (content & value of links) on that particular keyword term.