You have to look at how Google serves the results to qualify this.
For example we're ranked 2nd in the UK for "Business Web Design" and "Business Website Design".
Our home page title contains that keyword and the url contains the word design.
We also have an internal page for /business-website-design which ranks 4 pages down.
So Google can see that our site is highly relevant to that term, but it ranks the TLD (brand) ahead of the internal page - even though the internal page actually has the higher relevance and also the higher number of "business web design" related backlinks.
For broad searches such as "business web design" Google likes to serve TLD where possible and uses the weight of internal pages to rank the TLD appropriately.
A longtail search however is much more likely to show internal pages that are a highly relevant.
I'd say your homepage has a higher relevance. At the very least, it mentions the keyword more, hence ranking the home page as opposed to the internal page. Internal pages, automatically, have less weight than the TLD.
I partially agree to serving the TLD where possible, but it isn't to do with how broad the term is, but simply how strong the domain is overall and how relevant a page is. It's easier to rank a homepage than it is internal page BUT only by a fraction.
I could build perfect links to a page that has "Business web design" as the anchor, the page contains information about cars, but the hompage has business web design as the focus, then the homepage will rank. (Extreme example, and the website wouldn't rank anywhere near as well as it would with links to the right page). The internal page will rank for a little while until does a proper crawl of the website and realizes that it's not relevant.
It's how the link juice works and flows through the page, and how Google works.
One example I'll use is this one:
The third website down is an internal page and shows that it's down to how relevant the page is. In your instance, Google has decided that the homepage is the most relevant in terms of authority, content and links.
Unless I've wildly missed the point! Ha