I guess you were unlucky because http://support.apple.com/kb/dl1572 was blank yesterday and today it works!

for a couple of websites a newest version of java is required

The Apple version of Java you installed can be used only for Java applications, not for the web.
If you want to test Sweet Home 3D with Java 8, install Oracle Java 8 and run it with Java Web Start (to start the application from the SweetHome3D.jnlp file you'll download, click on the SweetHome3D.jnlp file while pressing the ctrl key, then choose Open menu item).