You do actually download the video and it saves in it the Temporary Internet Files folder. This is where you can get it from. The type of file is a FLV, so you will need a player, like this one download.com/FLV-Player/3640-2139_4-10505954.html?tag=tab_ur
How to get the file. (warning!! this is a little bit tricky, but not too bad.)
Watch the video you want to download, and make sure it loads in completely. (for IE7) Go to your Temp Internet Folder (Tools>Internet Options>Browsing History Settings>View Files)
Sort the files by name and look for the file named wUreHpivVKc.flv (This is in the case of your example above. For other files look in the address bar on youtube.com for the video you are watching and the name will be the last bit after v=, just with .flv on the end)
When you have found the file, right click and copy it. Then paste it which ever folder you want it to be.
If you can't find the video, it may be because you have not let it fully download (the little red bar that goes across), or you may need to refresh the folder, press F5.
If you have installed the FLV player I gave above, it should not play if you double click it.
I am sure there must be an easier way, but this is how I have done things for years.... Old habits and all....
Let me know how you get on.
Jake