You may be completely fine with not having a firewall to protect you from incoming traffic if you're sure that you won't open additional ports on your server. And if you do decide to open ports a software firewall (that's what you're relying on in this situation) may be okay. And additionally a software firewall may not provide you with nearly as much protection as a hardware firewall. There is a big difference and it sounds like your service provide is attempting to avoid dealing with the later.
That being said, I typically set up systems to protect the outside world as much as the inside. How sure are you that your server will never start sending traffic out into the wan? In a situation like that it's really nice to have a hardware firewall to avoid being blacklisted (should your server decide to send out thousands of emails on behalf of someone else).
Think about what you may want to protect.