It doesn't actually need to store it to log in again. The next time your phone connects to linkedin's proxy, it will provide the password again. Yes, this is basically the same as omnipresent, but not quite. If the servers are confiscated/stolen in a powered down state, the passwords aren't there to recover. You can immediately limit your exposure by not using the service. There are no backup tapes to accidentally go missing.
Also, while rare, the client could theoretically be using something like kerberos to authenticate, even over tls. The password exchange is secret, but the data contents would not be. I don't think the iphone supports kerberos, though.
(All this is not proof that they aren't your storing password, just that it's feasible for linkedin to merely pass it through. And possible, though not probable, for them to never even see the password.)
Also, while rare, the client could theoretically be using something like kerberos to authenticate, even over tls. The password exchange is secret, but the data contents would not be. I don't think the iphone supports kerberos, though.
(All this is not proof that they aren't your storing password, just that it's feasible for linkedin to merely pass it through. And possible, though not probable, for them to never even see the password.)