For a company providing critical computing resources, during an incident there should be one person responsible for managing incident response. It actually shouldn't be an engineer; the person's job should be to bug engineers as little as possible but provide periodic updates in a central location (a site of the form https://status.example.com) which is available to all customers.
Communication and coordination are important parts of incident response. Key engineers shouldn't be doing either. If an org doesn't have dedicated people to communicate with their customers and triage support during an outage -- especially one where a facility loses power -- they're doing something wrong.
When I was in a support role, I stayed up all night with the engineers during planned maintenance to answer questions, respond to tweets, &c. And if things went pear shaped, I'd already be up to speed.
Do you want their engineers bringing up the datacenter or answering up a bunch of e-mails with "we're working on bringing up the datacenter"?