Alpine ping: operation not permitted

I'm using Alpine (which uses busybox), and trying to get ping to work. First I tried installing iputils per https://serverfault.com/a/1001312 . No dice.

Then I found something that said I need to set the sticky bit, but it's already set.

What's going on?

/ # ping www.google.com
PING www.google.com (172.217.5.100): 56 data bytes
ping: permission denied (are you root?)
/ # which ping
/bin/ping
/ # ls -al /bin/ping
lrwxrwxrwx    1 root     root            12 Jan 16  2020 /bin/ping -> /bin/busybox
/ # whoami
root
/ # apk add iputils
fetch https://alpine.global.ssl.fastly.net/alpine/v3.11/main/x86_64/APKINDEX.tar.gz
fetch https://alpine.global.ssl.fastly.net/alpine/v3.11/community/x86_64/APKINDEX.tar.gz
fetch https://alpine.global.ssl.fastly.net/alpine/edge/testing/x86_64/APKINDEX.tar.gz
(1/2) Installing libcap (2.27-r0)
(2/2) Installing iputils (20190709-r0)
Executing busybox-1.31.1-r9.trigger
Executing glibc-bin-2.28-r0.trigger
OK: 49 MiB in 32 packages
/ # ping www.google.com
ping: socket: Operation not permitted
/ # which ping
/bin/ping
/ # ls -al /bin/ping
-rwsr-xr-x    1 root     root         60232 Oct 22  2019 /bin/ping
/ # chmod u+s /bin/ping
/ # ping www.google.com
ping: socket: Operation not permitted
/ # cat etc/os-release
NAME="Alpine Linux"
ID=alpine
VERSION_ID=3.11.3
PRETTY_NAME="Alpine Linux v3.11"
HOME_URL="https://alpinelinux.org/"
BUG_REPORT_URL="https://bugs.alpinelinux.org/"