Sorry, I have to categorically disagree with Sangeetac here. Kimberley, your understanding is entirely correct.
There's so much misinformation and misunderstanding about canonicalization, and there doesn't really need to be.
The rel canonical tag is ONLY to be used when there is a justifiable reason why the multiple duplicate pages in question should actually be reachable via different URLs. Unless such a reason exists, you should ALWAYS use a 301 redirect.
Put another way, duplicate page issues should ALWAYS be resolved using 301 redirects unless doing so would harm the user experience.
In the case of multiple versions of a home page, there is absolutely NO BENEFIT to the user to be able to reach that page via multiple different URLs. (In fact the multiple URLs could be confusing.) Therefore, the 301 redirect should be used to FORCE the user (and search engine) to the single version the site owner has decided should be the primary URL. Again, the other URLs are pointless, so the user should be blocked from ever being able to reach them. Using the 301 in this case has the added benefit of explicitly and automatically telling the search engines that all the redirected URLs for that page should be dropped from the index as they are non-functional. (And that's exactly what happened, Kimberley, as you saw default.asp and index.htm disappear from the index.)
The ONLY time you'd use a rel canonical tag in this case, instead of a 301 redirect, is if for some reason the site owner doesn't have sufficient access to the sever files to be able to implement a 301 redirect properly. In that case, a rel canonical tag can be used as a "better than nothing" solution.
The classic example of when to use a rel canonical tag is in the case of a page that lists a large number of products. That default (and therefore canonical version) version of the page may very well list the products in the order they were added to inventory. There may well be additional versions of the page, each at a different URL (often using query parameters, for example) which lists exactly the same content, but one page sorted by size, another version sorted by colour, yet another sorted by price.
Obviously in this case, 301-redirecting those additional dupe pages to the original page would be harmful to the user experience, because the user would never be able to access the content sorted the way they want to see it. So each duplicate version of the page has value to the user and therefore MUST remain available to the user, and therefore to the search engine.
In this case, the site owner adds a rel canonical tag to each of the dupe pages pointing to the primary (canonical) version, to make it clear to the search engine that the dupe pages are intentional secondary variations that should pass all their ranking value back to the primary page. But NOTE! Google themselves say they consider the rel canonical tag as a suggestion only, and will ignore it if they deem it incorrect or manipulative. So it is NOT NEARLY as strong an indicator as a 301 redirect which forces both user and search engine into the desired behaviour.
Sorry if that got a little long-winded, but once we get clear on the basic purpose of 301 redirects vs rel canonical tags, it becomes much more straightforward which to use when. The confusion usually stems from folks trying to justify using canonical tags for purposes for which they were never designed. They are not a panacea or a catch-all for fixing site architecture mistakes.
Hope that clears, rather than muddies the waters?
Paul