That design of lamp has been used in books to designate scholarly wisdom as far back as I can remember. I think you are putting too much emphasis on it being an "Arab" lamp. I believe the Greeks and Romans used similar lamps.
Here is a Typical Roman lamp.
No, I'm not. A clay pot is a far cry from an ornate metal lamp with ornate flair.
We have far better examples in our country's own short and distinctive history than to go back and find examples of why it "really isn't a Muslim influence" to put Aladin's lamp on a damned DoD logo.