It's much harder to get away with vote changing when there's a paper trail. The greater concern is the closed source voting machines, where you have no idea what's going on inside, whether there's an internal paper that matches your receipt, where touchscreens can be miscalibrated and a bunch of people who don't ask for or double check their receipt get fucked over, etc.

Edit: This might still be unclear. Some places have you casting your vote on a computer. Some places have you fill out a paper ballot and feed it into a counting machine. The second case, there's no mystery program handling the voting, it's still on paper.