DMZ isnt an open country that anyone can do whatever they want but the security is diferent from that you had applied to internal network.
DMZ "means" that you should allow SOME connection to be inbound (because you are serving someone out there). But all activities on DMZ must be controlled.
DMZ / Corporate network segregation is very good because it makes security manament easier than put all on the same network behind your firewall. I can say that because here its common that small companies (with no money) wants these kind of configuration (all behind, no segregation) and its harder to do than with DMZ segregation.

If you boss think that all ports should be open to DMZ, you may be suggest him to "refresh" his mind (very kindly pls). He is thinking about WAR, not IT