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Say I receive a phone call from a US school among top 30 in my field, offering me a PhD position, stating that the formal proposal should arrive in a week or so.
Am I wrong in assuming that the chance of the letter never arriving are zero almost surely?
Never assume. However, this sounds generally good. That being said, being accepted to a PhD is something that does happen, so I wouldn't know why it would be unlikely, as your question seems to implicitly assume.
If you are a frequentist: yes, you are wrong. If you are a Bayesian: there are no wrong assumptions, the question is how you will modify your priors at the end of next week.
