Whether in costume or not, Matt went with them and was killed in the explosion - sometimes in those situations bodies don't get found and it doesn't require a whole lot of detecting when a building came down, imo.

I think we might have very different opinions on what kinds of cover ups the NYPD would be willing to engage in. They're not a squeaky clean organization, irl or in this show. Whole departments cover shit up all the time. The team trying to dodge a Times news exposé after the fact might be interesting, though.