You may have noticed many websites host user-uploaded content on a different domain to their main site. Github delivers some things from githubusercontent.com, Google some things from googleusercontent.com, Reddit delivers some things from redditmedia.com and so on.
The reason they do this is to give a big layer of protection against the harms of XSS - even if user-uploaded content manages to execute arbitrary javascript on googleusercontent.com the that javascript can't access cookies for google.com as it's hosted on a different domain.
Some scoring guides rate XSS as very high risk, assuming you don't have this mitigation in place. resonious had the mitigation already ("it was under an odd domain that doesn't host any authenticated resources") so the XSS wasn't a very high risk.
With that said - some people will thank you for demonstrating how a small security problem can be escalated into an account takeover, but other people will call the cops on you for hacking their website or threaten to sue you. So I would say if you're reporting XSS it's reasonable to stick with an alert box, unless you know the person receiving the reports is reasonable.