swa66 - 6:36 am on Jul 31, 2012 (gmt 0)
Check what DNS resolves to for the host between their site and the rest of the world. It would not be uncommon (although it is ill-advised) to use the external domain also internally and serving more information internally and hence copying the external info in the private DNS servers. If the external one that is updated, only the internal ones do not see it and continue to point to an old instance.
Others reasons like content filters, proxies etc. can also exist, depends a bit on how their network is built.
If they're small it might be that the ISP they use used to host their website and has not removed the DNS service after they moved away from them for webhosting and/or DNS services and that soem old info was left lingering around.
Check on the logs of the server that you actually see their connection come in live.
-> if you have that, network, proxies, DNS etc should be relatively clean, and you should try to focus on the server - but from what you describe, you will not get there I'm afraid ...