The envelope will stay on the clip you selected to automate (it will be ghosted). The other flat lines will disappear when you go back to just showing clips. I think what is confusing is that when you select a clip and all the clips will sport an envelope. Ignore them. Just work on the one you want. The others will go away.
The Edit filter is actually working in the right way because you may want to edit automation on more than one clip.
The Edit Filter is your friend. Also the track Inspector is a great friend too.
BTW thanks Scook for providing the graphics and clear explanation.