Just trying to remove all ambiguity:
“dist_home”, “me” and “us” are at the local database.
The remote database “gets” the rows from dist_home [us/me] by sending us [dist_home/me] a select statement that asks for some rows each time it gets a row from dist_away.

My impression is that the remote database is sending us just the result in order to display it. It “gets” the rows from dist_home, performs the inner loop on-site and sends us the reult back.

I’m thinking about a kind of dynamic sampling parameter for remote queries. Lets call it remote_stats. If remote_stats is set to 1 only basic informations are retrieved from the remote instance (you already mentioned them) and as you set remote_stats to a higher value more and more information about the remote tables are requested from the other instance.
So the user can decide what’s more important: less network overhead or more round trips and probably a better execution plan.

Can you be more precise in which bit of information you are thinking of ?

The local database will request basic object statistics from the remote database (table stats, index stats, simple column stats) before optimising the query; but there are two “flaws” to the strategy:

a) It doesn’t request histogram data from the remote database

b) When doing the optimizer calculation it doesn’t allow any extra costs for round-trip time to the remote database. It simply uses the statistics as if the tables were all local tables.