How to use Finder's "Open With Application"? (Apologies in advance if the menu names aren't exactly right -- I'm not using Mac OS X in English, so I'm guessing at the translations.)

I was curious what the "screen sharing" shortcut had in it, so I opened up my ~/Library/Application Support/Screen Sharing/ folder, right-clicked on the "VNC Internet Location" (*.vncloc) file there, and chose "Open With Application -> Other".  Then I chose TextEdit.app.

I thought this would open the file (which looks like an XML plist) in TextEdit.  Instead, it switches to the Screen Sharing app!

I switched to TextEdit myself, and used File -> Open, and found the *.vncloc file, and it opened as a plain XML file just fine.

Am I misunderstanding how the Finder's "Open With Application -> Other..." works?
No, you're not. The Open with Application will do exactly as expected, open whatever file you've chosen with the selected Application. For your weird behaviour, perhaps you double clicked it, or it just bugged somehow and didn't catch the new application as the one it should be open with.