Hi Brian,
<blockquote> See, for example, http://www.greenpeace.org/aboutus/
Contains the phrase "As one of the longest banners we've
ever made" and has contained it since Greenpeace Planet
inception. Google is aware of this phrase only at an
alternate site that quotes it.
</blockquote>
I did a search on Google as follows:
"as one fo the longest banners we've" site:www.greenpeace.org
and www.greenpeace.org/aboutus/ appeared as the only result.
I'm guessing you didn't see it because Google filters out redundant results, but Google is definitely aware of the page. Click on the "repeat the search with the omitted results included" link to see all results.
I checked a few of the "deeper" pages in the Greenpeace site and then ran a search on Google for a phrase within that page, adding "site:www.greenpeace.org" (to limit the search results). And Google appeared to be aware of the them (atleast the ones I checked). Google also seemed to be aware of the various versions of the page (eg, /ships/ship-detail?ship... and /international_en/ships/ship-detail?ship...
Perhaps one of the problems is your ranking within Google, which is a separate issue. I know there are companies/software which can supposedly help in that department, but I don't know if they are reliable.