You only need an emergency fund if you do not have access to credit at reasonable terms.
Surely the relevant question is whether I'm likely to not have access to credit at reasonable terms during an emergency, no?
I don't really see many emergencies that can be handled by cash but not by a loan for cash. If you're solvent and people want dollars later, then they will lend you money. If you're not solvent, then whether your immediate liquidity is in credit or cash doesn't make a big difference since you're still not solvent. If nobody wants dollars later (say, asteroid), then it's unlikely that having dollars now is going to fix any emergencies.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.