If a system goes down when Meta experiences outages, can it be considered "on-premises"?

Why not? On-premise and autonomous/decentralized are two completely different aspects.

How so?

You can totally have an on-premise appliance that behaves like a black box, is remotely managed by the vendor and depends on their cloud services for even basic functionality. (Not saying that this is what WhatsApp's solution is – I've never looked into it!)

I wouldn't consider that to be on-prem at all.

That's called malware I think.

I think it's effectively some weird containerized WhatsApp client. The benefit seems to be that it provides end-to-end encryption between the company and the customer, unlike Meta's hosted version.

Wait, Facebook's whatsapp is also end-to-end encrypted, right?

It is, but for B2C messaging, there is a solution hosted by Meta that terminates the encryption at the gateway level (i.e. Meta can see the message content).

The alternative to that is the on-premise solution.