wordpress网站上的“主机”禁用mail()功能?

The contact form on http://www.allinsure.ca/contacts/ stopped working. I've disabled the form for now - it was created using Contact Form 7. Recently there has been a lot of email spam coming from that site, so my initial reaction is that the host may have disabled the mail() function. I called the host, and they said it wasn't them - everything was fine. Just to test, I tried resetting my wp-admin password... nothing. Here's the error:

The e-mail could not be sent. Possible reason: your host may have disabled the mail() function.

Seems like a host problem, right? I called again, argued a little bit, and left confused. It's not a host issue, it's something on the WordPress side.

Any help (resources, guesses) would be much appreciated.

Happy holidays!