So by that aphorism you mean we should get all the facts (such as by looking) before taking a risk (like leaping). Applying that to the unknown of possible massive voter fraud, we'd have to get the facts on its likelihood before deciding to go ahead with that kind of voting.
But what you're positing as the conservative move seems like another kind of leap, namely a leap into paranoia and conspiracy theories. You're saying the mere possibility of fraud or misuse should be enough to guide policy. I don't see how that strategy is justified by even a narrow reading of your aphorism.
Hasn't that kind of voting already been tried with no results of massive voting fraud? Haven't Americans already "looked" in that case, so that continuing with that voting isn't like leaping without looking?
What's the difference between harvesting those votes and counting paper ballots that have been put in boxes? Either way, the counter eventually needs access to the raw ballots to count them, so procedures need to be put in place to prevent tampering. In Canada, paper ballots are put in boxes, someone counts them, and there's been no massive fraud. So the "looking" has been done by trying out the system.
Or are you saying that nothing should even be tried unless you're absolutely certain nothing bad can happen. That sounds like a definition of paranoia. There's no certainty about anything, regardless of how much looking we do. If you can trust your eyes that look before you leap, why can't you trust all the elections that have already been done in which harvesters and counters have had access to paper ballots without committing massive fraud?
"One thing follows another" is surely an appeal to causality or induction, which was my point in the Oakeshott article. Otherwise, I think you're reading between the lines. Is it supposed to be an appeal to entropy, to system breakdown so it would be like saying "Shit happens"?