Everybody got the word. I remember when they found rocket launching gear in the dunes on Jones Beach about two days afterwards...and then we were told it was just for large 4th of July fireworks!
I don’t know how high the plane was, but if you’ve ever gone out of JFK en route to Southern Europe or other southern destinations (which I used to do all the time), you come out low, fly along Long Island, and then loop out over the ocean. In other words, normally, they would have been low enough for somebody on the ground to get them. Heck, I could practically count the dune grass half the time when we flew out of JFK.
It was low enough that the witnesses clearly described the plane being cut in half and the front part falling first before the back part. You can’t see that from the ground if your 30,000 ft up.