It turns out that in the absence of a specific binding, the server binds to IPAddress.Any. When a client attempts to connect, it's redirected to the server's bound address. Unless client and server are hosted on the same physical machine, there's really no point in ever using the loopback adaptor... which makes it a strange choice for default.
Before you create and register your TcpServerChannel, you need to set some options.
IDictionary properties = new Hashtable();
properties["bindTo"] = "dotted.quad.ip.address";
properties["port"] = port;
IChannel serverChannel = new TcpServerChannel(properties, new BinaryServerFormatterSinkProvider());
RemotingConfiguration.RegisterWellKnownServiceType(typeof(Explorer), "Explorer.rem", WellKnownObjectMode.SingleCall);
Voila! 'appiness should ensue...
PS. If for some reason the dotted quad doesn't appeal to your particular situation (e.g. load balancing), you can set two other properties instead:
properties["machineName"] = "load.balanced.server.name";
properties["useIpAddress"] = false;
PPS. I think the client will make always two socket connections, A + B. A is used at the start to do some initialization and get the address for connection B. B is used for meat and bones of the operation, and finally A is used just before they're both closed.