Why are some symlinks unreadable when their target is readable?

On Linux, I'm looking at /proc/1/cwd. This symlink is not readable as a normal user:

$ ls /proc/1/cwd
ls: cannot access '/proc/1/cwd': Permission denied

But /proc/1 is accessible:

$ ls /proc/1

After becoming root, you see that /proc/1/cwd points to / (filesystem root):

$ sudo ls -l /proc/1/cwd
lrwxrwxrwx 1 root root 0 Feb 21 12:56 /proc/1/cwd -> /

And of course the filesystem root is readable, as a normal user:

$ ls /

If symbolic links don't have any permissions on Linux, then why is such a symbolic link not readable, when its target (the filesystem root) is readable?