ohashi beat me to it. That's almost certainly a website that you've visited using retargetting. More info: http://www.bizreport.com/2010/03/google_adwords_finally_gets... . Article starts out "While Yahoo, ValueClick and other ad networks have offered ad retargeting for some time, Google has only just released it to their AdWords customers after twelve months in beta."
I don't have a screen shot, but I do get text pop-ups from Google on top of my YouTube videos with things from my search history. For example, "Is leg pain a problem in your life? Go to [...]." (This actually happened.)
Just yesterday I got one from SpecialTeas.com which said something like "We miss you at SpecialTeas, please come back."
The point is that it's not cool to be showing someone a YouTube video and then all of a sudden not only are there ads showing up based on my search history, but the ads are actually incorporating my search strings and purchase history directly into their text. Especially when these have to do with personal issues, medical problems, etc.
Is there anyone here who wouldn't be uncomfortable if they were in a movie theater with their family and friends and all then without any warning they suddenly started projecting your Google history and credit card purchase history from the last 5+ years? (Both of the examples listed were drawing on searches I had done 3 to 7 years previously.)
Not sure how you'd do this, but there's probably a way to prevent your Google cookies from being sent to YouTube at the browser level. It'd be an ugly hack, but a usable one nonetheless.
If he doesn't want his friends to see his health information, I don't think he'd feel comfortable linking to a screenshot of it showing up on YouTube...