A Search Engine Watch Forums thread has discussion on using the site exclusion tool within AdWords to block your ads from showing on some of the search network. In addition to that, you can use the site exclusion tool to block your ads from being displayed on most but not all parked domain sites.
Google runs a Google AdSense for Domains program that many AdWords advertisers find to be a waste of their money. So some like to exclude the ads from showing on those sites as well as other parked domain sites.
Essentially, it is possible to exclude most parked domain sites using the site exclusion tool. For technical reasons, however, some sites will currently require the assistance of the AdWords support to exclude, as you have noted.
So most of the time the site exclusion tool should work, if not, contact Google and they can make it work for you.
Forum discussion at Search Engine Watch Forums.