The property you are looking for is called "non-repudiation", which might be a useful starting point for additional research. However, as the link in StackzOfZtuff's comment highlights, this is NOT something that TLS provides (for the reasons given in the answers above, which remain true even now, 7.5 years later).
In general, there are two ways to achieve non-repudiation:
- The originating party cryptographically signs the data with a private key that only they know, but for which any other party can use the corresponding public key to verify the signature. However, inherently, this only proves that the originating party signed the data; to prove anything else (like when and whether it was sent, and to whom) you'd have to sign that metadata as well.
- A trusted receiving party (who can be yourself, but usually you want it to be a third party whom all concerned agree is trustworthy) receives the data, verifying that it comes from the originating party, adds metadata to this effect (and usually also when it was received), and applies their own cryptographic signature with their own private key to this data-and-metadata. Then, anybody with this trusted party's public key can verify the signature and - assuming they trust the signer - use that to be sure of the data's origin.
There are several third parties who do things somewhat like this. Certificate authorities are one such; they take some data from you (a Certificate Signing Request) and authenticate you (or your domain), and then add some metadata and their own digital signature to the CSR (turning it into a certificate). Anybody can take the certificate, read the metadata on it (such as who issued it), look up that CA's public key, and verify that this certificate belongs to the named subject, to the extent that they trust the issuing CA to have authenticated the CSR's subject correctly. This is the core of the Public Key Infrastructure that underlies all of TLS, among other things. Incidentally, since the signed certificate does identify the authenticated party (the subject or bearer of the certificate), it itself can't be repudiated; you can stop using the certificate at any time, but anybody can pull it out and prove that you requested the CA sign it, and they did so.
Another such category of trusted third party entity is timestamping services. These services (which may be run by people who also run CAs) take some data - generally a cryptographic hash of some larger data - and append some metadata (a timestamp and a signer) and sign the resulting blob with their private key. Any third party who has the timestamping service's public key, and trusts the timestamping service, can thus verify that at the time in the timestamp, the signed data already existed.
To protect data transmitted over a network from repudiation, you'd need a slightly different sort of service, though. ICanProve, linked above, appears to be attempting to be that service. However, this is only useful to the extent that every relevant party trusts ICanProve to be correctly authenticating the remote end of the session, not allowing tampering with the site before signing, not allowing anybody else access to their private key (which could be used to make fraudulent signatures), and (if relevant) to have an accurate clock for the timestamps. If you do trust them for all that, though, that's exactly the kind of thing you need!