You can make the vid embed in HD by adding &ap=%2526fmt%3D22 inside the tag to the end of the string of characters after the = .
I did what you described and it doesn't play in HD. It only has the option for the user to select once its started playing in non HD
[youtube_browser]4Yj0NLCXT58&ap=%2526fmt%3D22[/youtube_browser]
This is the code I used except I added $$$ before the code so it will be visible so go ahead and exclude those three dollar signs.
[$$$youtube_browser]4Yj0NLCXT58&ap=%2526fmt%3D22[/youtube_browser]