You don't need to get access to a lot of machines. Because the chain is long and obscure, there's no way to be verifiable, and even if there was that chain would require specialist infallible programmers to ensure nothing has been tampered with.

I'm not sure how you can argue that obscurity is a strong method of security when one machine in the country could be compromised, or the counting method code could be compromised, or the programmer verifying the code could be compromised, or the distribution system of voting machines could be compromised, or any part inside the voting machines could be compromised (e.g. the touch interface), or the voting machine remains secure during the voting period (i.e. voters are tampering with it on poll day).