Unless you heard the exact support call with a cited document by Direct TV where they can cite something I will call BS. The Airport express and extreme work much like any other router in their design - they dont have any special firewalls that a router from a different manufacture would have and even if they did, such a firewall can be modified.
However the Direct TV box is probably just doing normal IP traffic over port 80 or SSL - both of which the Airport device is going to handle just fine. Pretty much all the cable boxes I have seen either just plug in to the router like any other computing device would via wired or wireless. If your computer can openly surf the internet normally, the box should be able to operate the same. Airport doesnt do anything unique that would block normal IP traffic unless you deliberately implement rules otherwise.
Nothing that this tech says makes any sense to suggest that it is true.
Now their techs might not know how to configure the Airport, but that is something totally different. If it is an ethernet based connection to the router, it should work.