Do you see the same behavior if you use AGX 1750? I have found AGX 2500 to be very buggy. I know that 10.11 map services can be consumed in AGX 1750; I'm not sure about 10.2 services in 1750.
In my situation, I have "secure" map services on ArcGIS for Server 10.11. AGX 2500 is unable to even see services in secure folders on AGS. I need to use AGX 1750 to connect to a secure 10.11 map service, then create an NMC file for that connection, then add that NMC file to AGX 2500.
I experienced the same difficulty. I don't think ArcGIS Explorer can use services when adding the service using the web adaptor. I added my server (which is not publically accessible) to ArcGIS Explorer twice, it the exact same server but one is using the web adaptor and the other is bypassing it.
Now they are both added and can connect and I can even see my layers on the list but when I add it to the map from my web adaptor URL then it adds but doesn't show up.
However when bypassing the web adaptor and using 6080 with the fully qualified domain name with "/ArcGIS/Services" at the end, my layers show up on map. Hopefully this will help.