When an article gets killed, can you pitch it elsewhere?

Recently I was assigned to do a story for a magazine, and after a month of research I submitted and they decided to kill it. Most of the contacts were supplied by the editor and they were the ones that assigned me the piece; does this mean I cannot pitch it elsewhere? Or do I have to wait a certain amount of time before pitching to a different publication?

What really ticks me off is, the next day after they told me they weren’t going to run it, I saw a story about my exact topic written on their website by one of their staff writers.