Which of the following statements regarding Apex Web Services is correct?

The statement that Apex web service calls can be faster than making individual API calls is accurate because Apex web services allow for the execution of multiple logic components within a single transaction. When using Apex web services, especially within Salesforce, you can execute complex business logic and manipulate data in bulk without incurring the overhead associated with multiple API calls. This is particularly essential in scenarios where you want to minimize the number of round trips to the server, as each API call has its own latency and resource consumption. Therefore, consolidating operations through an Apex web service can lead to improved performance and efficiency, especially when dealing with operations that require multiple steps.

The other statements do not hold up because they imply limitations of Apex that are not true: Apex web services can indeed support custom logic; many implementations of REST APIs may require significant setup; and Apex methods are fully capable of returning lists or maps, allowing for versatile data structures in responses.