It works in Picard, FWIW.

This issue is probably linked to MBS-3697, and Picard works fine because it doesn't use Amazon web service (it guesses cover art URLs).

Which part of those changes do you think has broken this? Or do you think it's broken for all new ASINs now?

The following change:

Associate Tag will be a required and verified input parameter in all requests to the API

Yes, I think it's broken for all new ASINs.
http://musicbrainz.org/release/a88afa2f-cd23-4bab-be15-b950ac9b5d8e is broken

My userscript http://userscripts.org/scripts/show/39913 is broken too.

reosarevok confirms this is still broken - http://chatlogs.musicbrainz.org/musicbrainz/2011/2011-11/2011-11-19.html#T16-20-55-388831

As this is somewhat of a regression, I'm moving to 3mo.

Fixed with 970c8ee.