Belz...
Fiend God
Perhaps the word, 'spire', is the source of confusion, here. However, praise be to the forum gods, for now I can post URL's.
This is the spire/tower/whatever to which I refer: http://amanzafar.no-ip.com/WTC/wtc41.JPG. It is in the wrong place to be your "concrete core." It is in the right place to be an outer wall, as can be seen in the related sequence of pictures here: http://amanzafar.no-ip.com/WTC/
Actually, the "spire" does seem to be from the WTC1 core area, more specifically some of the core columns survived the collapse, which is an impressive demonstration of the towers' resiliency.