Hey yosawat!
Welcome to Apple Support forums.
I have been using your technique to download YouTube videos for a long time, and have now discovered it doesn't work all the time.
When you open the Activity window on a YouTube page, the link to the video usually has 3.4MB of 5MB or something like that on the right, with a link usually starting with on "http://o-o.preferred.exetel-syd1.v5.lscache7.c.youtube.com/" the left. If this is the case, click it once with your cursor, then copy it into QuickTime. Press Command-U. It will open up a dialogue. Paste it into the text field and hit enter. When the progress bar for your video finishes loading, then hit Command-S and save it!
If there is no 3.4MB of 5MB etc., then there'll be a bunch of links like i mentioned before. It's usually the last. Use the same method as outlined above.
If not, please reply and describe your situation. I'll try to help more from there!
Hope this helped, xeniqillu