I reproduced the error. If I use "sudo find . | cpio -o -H newc | gzip -9 > tinycore.gz" I get:
cpio: ./usr/sbin/visudo: Cannot open: Permission denied
cpio: ./usr/bin/sudo: Cannot open: Permission denied
If I go into root with sudo su first and run the command, it works fine. I thought they were the same thing, but guess not.
i've experienced issues i would call similar, but a bit of experimenting helped my understanding. (that's assuming i'm right. if i'm not, it didn't help my understanding.)
for example, one might think:
sudo mkdir /tmp/sudotmp && cp /mnt/sda1/* /tmp/sudotmp would copy all files from /mnt/sda1 to /tmp/sudotmp, even if they can only be read by a superuser. actually, the cp command is not sudo'd.
i suspect (you'll have to figure this out) that cpio and gzip as you use them do not have root access. perhaps using sudo before cpio and gzip will help. it may at least explain your message.