indicates that ping should run as root, if owned by root (mine is). That would seem to make the use of sudo irrelevant, but it's not in my case.
I also looked at the ownership/permissions of the devices that the interfaces are being created on. The devices are created as
crw-rw-rw- root:dialout /dev/ttyUSB#
and the symlinks created for them from the udev rules show up as
lrwxrwxrwx root:root /dev/USBModem#
All users are part of the dialout group. I'm using the symlinks for pppd, but my understanding is that they are passthrough for permissions to the actual devices, so I wouldn't think that root being the group for the symlinks would matter. Strangely, changing the GROUP or MODE in the udev rules has no effect on the group/permissions of the symlinks.