I think the site is referring to some service/site that got hacked recently and that you signed up for with the first-name@[domain].com email adress and not to the email account itself.
It should tell you which sites were compromised such that you can ID if you used your email at any of said sites.
Just saying ambiguously that there was a site which may have been compromised out of the 2 billion sites online is laughable.
In fact, I would say that prompting the average person to change some passwords either way, is a good thing.