Simplified, there's two layers to data protection, physical and logical. Linux or basically any correctly configured modern operating system provides logical protection, i.e. access under the running OS is only granted to authorized users. Granted you can still put holes in here, e.g. a webserver is misconfigured and allows access to any user to all files it can read. However, from the OS perspective, everything is fine, as the webserver can still only read what it's allowed to.

Data encryption protects data at rest, i.e. when no operating system enforcing the logical protection is running. The case has already been described so I'm not gonna repeat that here.

It's important to understand that in general, these two measures are completely seperate from each other. Device encryption won't help against logical attacks, and logical protection won't help against offline attacks. You need both if you can't rule out an attack vector completely (i.e. your server sits in a secure safe that can't be opened by anyone not authorized to, then encryption might not be necessary).