Are HTTPS web sessions non-repudiable? (This is probably a basic question, and may be a duplicate; if so, just let me know.)

Suppose there are two clients A and B, and some server C. Suppose B and C establish an HTTPS tunnel, and C sends a response to B. And suppose B records the response, and sends it to A.


Can A verify that the alleged response from C was actually sent by C?


This is essentially equivalent to "Are HTTPS responses non-repudiable?". As far as I am aware, HTTPS only provides a secure channel, but does not provide digitally signed traffic.

Motivation

I'm tentatively planning to create a social network add-on which would allow users to flag other users who have sent them offensive material via private messages. I would hypothetically run a web service which would receive flag requests, and in order to avoid spam flags, I would need some way for the flagger to voluntarily send me a minimum but sufficient amount of information to verify that the private message actually exists. 

In this scheme, I am A, the flagger is B, and the social network is C. 

Is there any sane way to do this, without compromising the flagger's security?
No you can't prove that C sent something.
The only thing you can reliably prove to somebody is that somebody at some point had a HTTPS connection to C, by presenting the key exchange.

You can't prove that C send something because the record layer is symmetrical, meaning everything C sent, could be forged by B as he has to have the neccessary keys. 

To understand, let's quickly recap how TLS (the security layer behind HTTPS) works:
The server and the client negotiate a shared secret using the key-exchange which also proves to the client that he is communicating with the correct server. Both parties derive four keys (2x authentication and 2x encryption). The data you consider is symmetrically encrypted and then symmetrically authenticated meaning the receiving party can as well construct this exact message using the symmetric methods (by encrypting and authenticating the message with the appropriate keys). If the user presents you with a full transcript of his side of the key-exchange and communication you can't be sure if he forged the claimed message or if the server sent it legitimately as he must have the keys for that or he couldn't have received the message in the first place.