No, I saw that too, that she says she was reading over letters between Kirk and Finney that convinced her he couldn't have killed him. She makes a point of having to have to tell him before she breaks down and cries. It made it to the screen somehow. Though so much was cut during syndication to cram in commercials it's a wonder there was any story left at all sometimes. It's wierd to see cut scenes you never saw before 40 years later like that weird scene in the Honymooners where Gleason addresses the audience directly live to say Merry Christmas.
We do have the scene in the Teaser with Jame--the "I wanted a good look at the man who murdered my father" scene. We also have the later scene where Jame tells Cogley that he needs to get Kirk to accept a ground assignment because she read some old letters and never realized how close Kirk and her father were. (So viewers are remembering correctly: that scene is there.)
But the episode doesn't have the following scene from the script--from right when the court reconvenes to rest the case and hear the verdict, just before Spock and McCoy rush in:
ANGLE - KIRK, COGLEY
Kirk is doodling on a pad. Impatiently, he throws down the pencil. Cogley doesn't seem to notice.
COGLEY
Jim. . . how well do you know that
girl? Jame - Finney's daughter.
KIRK
Since she was a child.
COGLEY
(musing)
I suppose that might explain her
attitude. Curious though - children
don't usually take such a dispassionate
view of the death of a parent.
KIRK
She didn't at first. She was
out for my blood. Almost
hysterical. She kept saying:
murderer - murderer.
COGLEY
(almost a take)
Why didn't you tell me that before.
KIRK
I didn't think it was important.
Is it?
ANGLE IN ON Cogley.
COGLEY
(thoughtfully)
I don't know yet.
(It looks like someone realized that this is pretty much the same thing as Cogley's "No, but I might be getting ready" scene from a little earlier.)
But probably the most strightforward scene about what happened was in Act 4--right when Cogley leaves the bridge to tend to a matter "of vital imporance to this court." He pauses briefly to have a quick sidebar with Kirk:
TWO SHOT - COGLEY, KIRK
A conference between lawyer and client in the courtroom, which no one else can hear.
COGLEY
It's in your hands now.
KIRK
At this point, I'll try anything.
(incredulously)
But the idea of Finney being
alive --
COGLEY
I began to suspect that when
you told me about the change of
heart his daughter had about
you. If she knew he wasn't dead,
she had no reason to blame you
for anything.
KIRK
But how could she know?
COGLEY
You said she had been reading
her father's papers. . . probably
the general tone of what he had
written. A man suffering delusions
of persecution wants to set down
his complaints. She read them
. . . she knows the kind of man you
are. . . and she's fundamentally
fair and decent.
(beat)
Or maybe it was just instinct.
Thank God there's that much
of the animal left in us.