In my scenario, a machine knows the local exchange price as of 0ms ago (instantaneously) but knows the remote exchange's price as of 5ms ago.

You are saying it is better to know exchange A's price as of 2.5ms ago, and exchange B's price also as of 2.5ms.

But why? Either way you are ignoring 5ms's worth of trading activity. Either 2.5ms on both exchanges, or 5ms on one exchange.

Edit: I think I understand the advantage - see my edit #2 in my post above.