In theory, you are correct, in practice, not so much. I am involved in a business systems analysis project at work right now and one of the major elements is email deliverability rates. There is a significant gap between reported non-deliverables and actual. If you are counting on reported non-deliverables and following up only with those, you are going to miss a ton of people because there are a lot of ways that email is reported as non-delievered but is never seen by the target.

We have difficulty with purchase receipts that, because of the status of my employer, are held in company records, so must get through. This seems like a notification of similar importance. Our experience is that relying solely on email for critical documentation, especially that with financial implications, is folly.