What characteristics, specifically? If anything really was found, there's no chance it resembled trinitite in any fashion other than "looks like melted glass".

And, given that the location of Sodom is still unknown, if it existed at all, the story is probably total crap. And I only say "probably" to be nice.

If something significantly resembling trinitite was found near the Dead Sea, it would be an indication of some sort of nuclear explosion. Potential evidence of a nuclear explosion in the Middle East -- especially from two thousand years ago -- is the sort of thing people want to hear about.

And, as a less political rationale, if Sodom were discovered, and hot melted glass was found there, it would definitely make the papers. The discovery of the location of the ruins of Sodom would get a mention on CNN or Fox News; the discovery that something big, bad, and possibly Biblical happened there would make headlines.