Pings are just ICMP echo request/reply.
The ID and sequence number are in the ICMP header, if they were stripped then the requesting device would not be able to match up the reply (so the ping would fail), can't see there's much else to strip.
Can you try a packet capture on one of the affected interfaces, maybe it'll shed some light on differences between sites?
Tbh it sounds like a bug to me, if the ping succeeds it means the device that sent the echo request has received a matching echo reply, so it should be able to calculate the time difference.