The cross-post settings that one sets on the Other Sites page only applies to updates made through the update page, not through any other client

That makes sense, otherwise you could end up with more than one of the same post, if the client crossposted but then the sites crossposted as well.

It reminds me of a couple of people I know who briefly had Twitter set up to post to their blogs, but also had their blogs set up to post to Twitter automatically when it's updated...all it takes is one genuine tweet which gets posted to the blog, then an automated tweet saying the blog has been updated, then the blog reporting that tweet again, and on and on. It's hilarious, but pointless.