As I said, users had cases when the plumbing (messaging system) recovered and delivered messages after +40 days of network partitioning. Correctly written apps completed the business process associated with those messages as normal, no special case. Humans can identify and fix outages and databases can easily outlast network outages (everything is durable, transacted, with HA/DR). And many business processes make perfect sense to resume/continue after the outage, even if it lasted for days.
[0] https://blogs.msdn.microsoft.com/pathelland/2007/05/20/soa-a...
[1] http://download.microsoft.com/documents/uk/msdn/architecture...
Approaching exactly once delivery asymptotically is possible. Your parent poster's point is that this is one where you can get so close to exactly once in order that in practice you never violate for years and years.
In other words, to reliably agree on a system state (whether message id was delivered) you need the system to be Consistent. And per CAP theorem, it cannot be Available in presence of Partitions.
So other people you're referring to probably talk about distributed systems.