The trickiest situation I can imagine would be, for example, ordering fuel delivery for the backup generators at a private hospital.

But I can't imagine that being a problem if (1) it's done during a civil emergency and in support of that emergency, (2) non-HAM communications are not available and the order is time-sensitive, and (2) the order is done or approved by a government emergency management official. If current rules preclude it I'm pretty sure the FCC would issue a clarification if asked.

Another trick is whether the operator is allowed to have only "general knowledge" of the messages or must have "specific knowledge". If the FCC holds the operator responsible for each word spoken then every email or SMS would need to be pre-screened by the HAM. I would again bet that at worst the FCC would favorably clarify this for civil emergencies.