Hello!
I have the same issue (I guess ArmA 2 and 3 is using the same method to do this). Looks like the client is using ICMP to "obtain" the ping value when it is started as admin.
22:47:03.866071 IP 83.xxx.xx.xxx > 89.160.xx.xx: ICMP echo request, id 3368, seq 39430, length 14
22:47:03.866140 IP 89.160.xx.xx > 83.xxx.xx.xxx: ICMP echo reply, id 3368, seq 39430, length 14
(Well, it sends the request to my NAT since I don't redirect the ICMP traffic, but yeah, that doesn't matter).
If the client isn't started as admin, I don't see any traffic at all directly from the client that is trying to retrieve the ping from my server. Guess it goes through some other servers?
I have searched in many topics but haven't found a solution yet. Some people say "forgot it" if you are behind a NAT (in my case, a debian box), but that doesn't sound like a solution. I know we are not alone.