Sure thing! One of the things that helps me sometimes is re-arranging things visually.
A real divider:
Input o----vvvvv----o-------------o Output
|
|
Z
Z
Z
|
|
o
Ground
The bad one:
Input o-------------o----vvvvv----o Output
|
|
Z
Z
Z
|
|
o
Ground
Looking at it this way, it might be a bit easier to see that in the good circuit, both resistors can be in a Kirchoff voltage loop that includes the input, while in the bad one they can't.
(Edit: it appears I don't understand linebreaks on HN, so things are gonna appear garbled until I fix it.)
