Of course it isn't coincidence. It's not like there's a major shopping season (when people often buy new electronics) that might be influencing both Google's and Amazon's schedules or anything.
Interesting point, especially considering Google specifically said the source would not be available until the Galaxy Nexus was out.
>year's backlog
This is inaccurate, they have been releasing patches and updates for other versions of the platform over the last year.
They did skip Honeycomb, which fits your Amazon theory, mind you, from the reviews I have read the Fire would not benefit greatly from ICS as they Frankensteined the Android experience.
The Galaxy Nexus is hitting stores in the UK on the 17th so the release is only a few days early. It wouldn't surprise me to find out that they got done a little early and decided to "push the button" anyway.
It won't be any more difficult for Amazon than it will be for any other OEM; phones are merging in from 2.3 as well. And that's making the assumption Amazon actually cares about being in sync with AOSP.