I think everyone knows this who owns a domain. Probably people say this because (like I do too) they have all the control over the name. If I rent an apartment, I do have to consult the owner to make major changes.
I think people who get their email on their own domain generally consider it as their permanent home and don’t think about what will happen when the domain no longer is registered to them. Using the apartment rental analogy works up to a point. With an apartment you can get the postal service to forward your mail to a new address. With a domain name there is no way to get this to happen. Whoever holds the registration controls the MX record and can do whatever they want.
In case of death it's indeed an issue if someone isn't planning ahead.
With grace periods of the domain expiry process it's quite safe. People have plenty of time to recover it. It's also hard not to notice if your mail stops arriving.
