Asymmetric NAT'ing

I think I'm not fully understanding asymmetric NAT'ing...

Server A has Inbound NAT all ports/applications via Public-IP A.

Server A traffic is routed and Outbound NAT'd via Public-IP B.

Remote Host A pings Server A via Public-IP A and gets a reply from Public-IP A.

Server A pings Remote Host A, ping is received by Remote Host A from Public-IP B.

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Why is the ping from Remote Host A -> Public-IP A received by Remote Host A via Public-IP A and not Public-IP B?

Wouldn't Remote Host A get reply packets from Public-IP B and drop them (because it never sent echo packets to that IP)?

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*EDIT: I see similar behavior for any TCP connection via telnet from Remote Host A -> Public-IP A. The connection establishes and I see src/dst packets for Public-IP A only.