Their website might have gone down but I'm told that their underlying service is redundant across multiple availability zones.

Perhaps they should do the same for the website just to instill extra confidence, though.

I didn't get any SMSes or calls from PagerDuty even though I see 4 incidents triggered in the PD web UI. Although that could be due to Twilio going down.

We (PagerDuty) were down for a bit. We will move off of AWS asap once the dust settles.

Why move off, why not just replicate your service to another provider as well?

There's a good reason for that: when AWS has problems, we are under very heavy load because many of our customers are on AWS. The last thing we want to do at that point is an emergency flip to a secondary provider.

Is it just their user facing website that's hosted on EC2? Or do the pages originate from EC2 as well?