Are permissions set in the 'Get info' screen when right clicking on a file enforced cryptographically? If not, how are they enforced? Could anyone, for example, boot of a live OS on a USB stick and edit file permissions?
Filesystem permissions are not cryptographically enforced. On top of that, no general purpose OS currently has an implementation that would allow you to do this.
If you gain access to a filesystem on a machine where you are in control, you will always be able to read, write and modify at will. Keep in mind that gaining access means you need to be able to physically interface with the system and have access to unencrypted content. On-disk encryption for removable disks would prevent you from accessing or manipulating the data, but that is outside of the scope of the filesystem.
The file permissions are only enforced by the operating system. If you boot from another OS (where you have
root user access), you can read anything.
Of course, if the disk is encrypted (research Full Disk Encryption), then you would need the key to decrypt it before you could mount it. On a Mac, the disk encryption key is typically protected by the users password and decryption is handled during login.