If your IT guy can't do what you want, get him fired because if he can't get Wordpres working then he shouldn't be working in IT like that. I can see big problems if you can't get access to the file system for this area. That makes it almost impossible to do the standard things like installing themes.
From what I can see EAsy DNS doesn't do any site hosting. They only look after the DNS records for domain names, so all they'll be doing is pointing your companies domain name to your internal servers. This is good because that means that your IT guy will be the one to go to with any issues that you need sorted out.