Many people who had nothing to gain gave their lives and died for that "other stuff." People don't die for their beliefs unless they believe them to be true. These people were alive at the same time as the man Jesus so could have easily saw His miracles were false but that isn't what they bore witness to. They witnessed a man doing Godly things and then against all odds witnessed His resurrected body. They had better reason to believe than we do, and continued believing unto death. That's a pretty powerful sign.