Hi Andrew.
When I began looking at this question I did not immediately realize it was a ccTLD of .au so I looked in Google.com and the results are quite different and probably more in alignment with what you would expect. The question is how much of the difference is attributed to the fact Google.com's algorithms are more updated with respect to Panda and other changes (it seems quite a lot), and how much of the difference is due to geographic targeting differences.
When I look at the site if I were to make a case to support the Bunbury association I would point out five items:
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Bunbury is mentioned on the page
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Bunbury is not in the footer, but above the actual footer. You could say the site has two footer areas, but clearly the area where Bunbury is located has more value then the smaller footer area below it.
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Bunbury is in bold. More to the point, the page has no h1 tag, no italics used, no alt tags used, and only a total of 3 words in bold, so this emphasis has a lot of meaning. This isn't a case of a page with 100 attention getting mechanisms are in place with the emphasis weight divided.
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Bunbury is one of only two locations mentioned on the page, Bunbury and Perth. This isn't a case where a page is trying to stuff 20+ locations to manipulate associations. It seems quite authentic.
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A phone number is listed right below the Bunbury mention. I have no familiarity with Australian phone numbers but I presume it is a Bunbury number.
With all of the above considered, the question is whether that is enough for Google to associate Bunbury with the page. I understand your position that it isn't much. Google clearly feels it is enough. I would also share it appears very authentic so clearly Google got it right, but the question is how?
Well either the above alone is enough, or there are some external factors influencing the decision. Some external factors are:
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You are correct the backlinks do not show any use of Bunbury in anchor text, but there are many links which have addresses in the URL linking to the page. These linking pages clearly have a strong association with a particular physical location, and this can definitely be understood by Google.
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Google could consider the site's contact page which shows only two locations, one of which is Bunbury. In addition to the information from the home page, there is also a Bunbury fax number, a Bunbury physical address and an e-mail to the bunbury office which shows as bunbury@.
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The domain ownership and hosting records do not show any Bunbury association and there is not any Google Places listing, but Google could also access business records such as business licensing for example. Google's algorithms are a closely guarded secret and we simply do not use what information is and is not used.