No it doesn't. The write is not durable in other datacenters when the client acknowledgement is returned. It is still possible to lose data.

It does. The three AZs they replicate across are just as good as anything else someone typically calls a "datacenter." Amazon itself operates retail out of one region and uses multi-AZ as a fault tolerance strategy.

It won’t lose data in the event of a data center failure. Each of the replicas is in a different AZ, and at least two of three have to durably write the data before the put succeeds.

An AZ is not a datacenter.

This is what I was referring to: An Availability Zone (AZ) is one or more discrete data centers with redundant power, networking, and connectivity in an AWS Region. AZs give customers the ability to operate production applications and databases that are more highly available, fault tolerant, and scalable than would be possible from a single data center. All AZs in an AWS Region are interconnected with high-bandwidth, low-latency networking, over fully redundant, dedicated metro fiber providing high-throughput, low-latency networking between AZs. All traffic between AZs is encrypted. The network performance is sufficient to accomplish synchronous replication between AZs. AZs make partitioning applications for high availability easy. If an application is partitioned across AZs, companies are better isolated and protected from issues such as power outages, lightning strikes, tornadoes, earthquakes, and more. AZs are physically separated by a meaningful distance, many kilometers, from any other AZ, although all are within 100 km (60 miles) of each other.