Which statement is true regarding the security context of Apex web services?

The correct statement regarding the security context of Apex web services is that Apex web service methods run with system privileges. When an Apex web service is accessed, the operation occurs in a system context, meaning it bypasses the usual permissions and sharing rules that would normally apply to a specific user. This allows the web service to operate with full access to the Salesforce data, regardless of the permissions assigned to individual users.

This system privilege context is particularly important for applications that need to perform administrative operations or access sensitive data without being limited by user permissions. Such functionality can be crucial for integration scenarios where a web service must retrieve or modify data on behalf of multiple users without being restricted by each user's individual access rights.

In contrast, the other options present scenarios that do not accurately reflect how Apex web service methods operate. They either suggest that object permissions of individual users are respected, which does not happen in this context, or that there are no security considerations at all, which would overlook the importance of managing how and when these privileged operations are used. Additionally, suggesting that the 'with sharing' keyword is always required for web service methods is misleading; while specifying 'with sharing' enforces sharing rules, the system context of web service methods specifically ignores those rules.