The "state of registry" of aircraft and the implicit jurisdiction in matters of wreckage recovery is rooted in international convention, partly to deter looting and plunder by any parties so inclined.  We might stop and think how we in the United States would feel if a Boeing 777 of U.S. registry had gone down in international waters and a couple of years later, after our own search efforts had come to naught and ceased, a private venture or another country such as the Russian Federation or (gasp!) North Korea decided to conduct a search for "our" aircraft.  Would we just shrug our collective shoulders and say, "Well, okay mate.  We've done our bit.  You go right ahead."?   Would we really? 

As for why Malaysia might be hesitant about Ocean Infinity's offer, perhaps it's due to the as yet undefined amount of the "reward" the company has suggested as its due.  It's something to think about.