Heh, spam comes from spammers 🙂
They like to use any MTA that's not been updated, like his, perhaps. Sendmail is not near as bad about it as, say, ESMTP, which is used by many of the lard-brained ISP's 'round here.
Also, if it's Linux/BSD there are some server functions that usually use Sendmail for logging, etc. so I wonder if it's really off. That said, it's quite likely that he's disallowed user 'nobody" from accessing it. I'd try it, anyway, depending on HOW he's shut it off, it still might work. I think that's what planetsim is betting on --- that using a different username than 'nobody' in the from field might help. It's possible....
There is, by example, this note in the PHP manual
I would also question whether having Exim as the MTA will make a lot of difference. As I mentioned, lots of servers use mail, and it's likely that they system lets them use whatever MTA is running....