Here's a method I've used -- create a separate copy of the page on your server, and dedicate it just to that link. Add a 1x1 clear gif to the bottom of the page, and call it from the 3rd party's server. They can track the hits on the gif.
If the 3rd party records are periodically bumped up against your server records to validate the referer records and filter out hits from in-house or other accidental sources, I think you would have pretty good accuracy. It beats having the 3rd party serve the whole page, IMO.
You might also have the third party serve your entire page in a 100% frame -- then the link goes to their server and they get the referer information. However, if their server hangs, then the whole page hangs, instead of just the 1 little dot.