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This question already has an answer here:

If I were to capture a TLS session (and shared secrets) between myself and a web site operated by another party, could I later use the HMAC (or something else?) to verify to a third-party the authenticity of the downloaded data, i.e. prove that I did not alter it?

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marked as duplicate by Sjoerd, Community♦ May 25 '17 at 12:25

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • Thank you to those who pointed me to the duplicate questions. I'm confident now that TLS alone cannot provide assurance to a third party that a session occurred as any party might claim after the fact. – Dave Begonia May 25 '17 at 12:35
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Note that your description is missing an important party: that to whom you wish to prove you did not alter the message. The question really is, can that party trust you not to produce a message you didn't exchange with the other party in the TLS session.

The answer is no, because you have saved the key, and thus you can generate valid tags for any messages as you like, which you might not have sent to the other end of the TLS connection.

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