That's What She Said Quote

Okay, I'm sure most of you have seen this T-Shirt before.

But I got to thinking about it the other day. It is obviously a reference to the time-honored tradition of That's what she said in response to any kind of innuendo or lewd comment.

However! Wouldn't it be more accurate for the quote to be:

"That"
     -She

I know it isn't as apparent what the joke is that way, but in the context of the line, the hypothetical "she" never said "that's what." What she actually said is "That" in reference to the comment before.

Is this right? or is the T-shirt in the right here?

Solution 1:

The meta-humor lies in making reported speech into quoted speech, as a play on words. The original "That's what"—She renders as

"That's what," she said

Your alternative "That" — She reads as

"That," she said

or

She said, "that."

If you turn this around and make it indirect speech again ("That" is what she said), then it wouldn't be recognizable at all as an attempt at humor.