If the V.P. resigns to become president, it's not "they" who appoint a new one, it's the new president who nominates a new V.P. subject to confirmation of both houses of Congress. So if McCain dies, and Palin becomes president, she gets to nominate her successor.
ETA: Ford's situation was different than the hypothetical we're talking about. Nixon didn't die, so a backroom deal was made for the VP to resign first. Nixon nominated Ford to replace Agnew, and then Ford succeeded as President when Nixon resigned. . .and of course granted Nixon a full pardon. (Among other things guaranteeing that Ford would not win an election to get his own term.)