Nope, urls are fine, and I've pretty much ruled out code/server issues. They're using IE9 which I haven't been able to test against (though as mentioned it's all working from staging for them). If it hasn't cleared up by Monday, I may have to do an on-site visit to check myself what's going on.
Tested in IE 7 & 9 here http://browsershots.org, and from another external network (wifi at coffee shop) All loaded it fine. Also ran it through several proxy sites, no problems.
The only time I've seen something similar to this was when a sites proxy server was mashing the headers in the request. In that particular instance, it came down to a GZIP compression issue.
(For anyone who cares about the specifics, this particular site returned a GZIPed page regardless of what was asked, and the proxy server was then stripping the encoding header on the response confusing some browsers)
Turns out we were talking about two different pages with similar names and urls, and not bothering to read each others' emails or click the links in them. Neat, huh?