hechsher certification - Claims on food labels: says who?

Sometimes a food item under rabbinical supervision claims on its package label not only to be under that supervision but also to contain only yashan grain, or to not contain sh'ruya, or to contain only chalav Yisrael, or to be m'vushal (if wine). I've always assumed that the agency whose certification mark appears on the package is also attesting to the other claim; but is that true, or does the certification mark only signify kashrus, with the other claims being only the manufacturer's?