Mystery Mirror/Mirroring My Client's Site Is On Another Domain But Why?

I'm having an issue with a client site and I am not sure what to do at this point. Conversations with the host (GoDaddy) haven't led to a solution and to be honest, I'm not sure it's their issue to handle although I will be firing off an email to their domain dispute department shortly. I spoke with a couple of supervisors there and they were as baffled as I am.

Here's the situation:

When people Google the name of the client's business, it returns their site but on a different domain. The entire site is there, nothing is changed but the URL. It's like having an unintentional mirror site except that none of the forms work which is what tipped off the users that something was wrong but of course, they don't notice that they're not actually on 'www.clientsite.com' so they think it's just a form error when in actuality, they're not even at the right domain.

There is really no way for this other domain to profit from mirroring the client's site; it's just a business profile type of thing with a few forms for contact, employment applications and vendor applications. No secure info is transmitted other than perhaps the occasional email address but we're not talking a heavy volume site, it's a niche market and really not something that would be a typical target. There's no eCommerce, no subscriptions, no financial info.

I'm at a total loss. Could this happen if this other site is hosted on the same server as my client's site? Could it be an actual error of some sort or would it have to be intentional?

The whois for this bogus site leads to DomainsbyProxy.com and I'll be sending them a letter as well but I'd really appreciate any input you all might have on HOW this could happen. Should I also contact Google?