Hi! Joel, I tried (literally) the same ping command on one of my networks with a rooted tablet, and got the exact result you note. Then I tried: sh ping -c4 www.google.com on my other network with an unrooted phone and it worked fine.
There are several possible variables. My wired router (the no-go) was set up to block "ping-packets" as a security measure. There could also be some differences in how ( and which) busybox was installed. I also recall reading something recently (as you did ) about 'ping' requiring privilege on newer Android versions, but several apps on the Play Store preport to offer 'ping' results. I hope this is of some help. I don't see Digest responses right away, so possibly you've gotten more exact answers already. Good luck, James Gere