According to my observation, there are at least two types of using "Not that....". And my question is: what does "not that" mean in its second type of usage?

In the first usage, "not that" is followed by a structure-complete sentence or expression.

Example 1:

I've been teetering down my twittering and self editing my Facebooking lately. It's not that I don't have the urge to write things. It's just I have to fight the urge to write really inappropriate things that maybe my old High School English teacher doesn't really need or want to know.

Example 2:

It’s not that I don’t care about football. I just don’t care enough.

In the second usage, "not that" is followed by an object-missing expression.

Example 3 (from Fringe):

Olivia: Anything to do with metamorphic ability? Peter: Not that I can tell.

Here, tell is a transitive verb and its object is missing.

Example 4 (from Fringe):

Olivia: Were you involved in...? Walter: Not that I recall.

Here, recall is a transitive verb and its object is missing.

I understand that, in the first usage, "not that" sort of means "it doesn't mean...". But I'm not sure, in the second usage:

1. Why are objects of transitive verbs missing?
2. What does this type of "not that..." sentences mean here?