You can lookup by PUID with the web service. For AcoustIDs there is no such possibility atm.
This is more relevant now, since we depredate PUIDs in http://blog.musicbrainz.org/?p=1832

The acoustid.org Web Service only allows lookup by actual fingerprint:
http://acoustid.org/webservice

This should probably be implemented on the acoustid.org side, since that is where the data is. The corresponding ticket is:
https://bitbucket.org/acoustid/acoustid-server/issue/7/web-service-cant-search-by-acoustid

This was originally requested in:
http://stackoverflow.com/questions/15571893/search-for-acoustid-on-musicbrainz