From what I've read and heard, it's pretty advanced stuff. In some of the clips I've listened to they'll hear a random excerpt of Romantic period music (say, 20 seconds worth), and the person will immediately play it back on the piano at tempo.

Now, if you played back the intro to Beethoven's Pathetique Sonata, would the savant give the full duration to that tied dotted sixteenth note from the first chord? Could they play back the first page of Ligeti's tempo fugue etude? I'm not sure, but what they do is already well beyond what even trained professional musicians can achieve.

Digression-- our idea of what constitutes "advanced" can get a little out of hand with myths that have been handed down over the years. Even Mozart "cheated" every now and then. One contemporaneous composer noted that when he requested that (child) Mozart sight read a difficult piano sonata, Mozart improvised the development section because it was too difficult to sight read it.

In at least one case I’m aware of, it’s the savants themselves. Treffert wants his pet theory to be true so badly that self-attestation is enough for him to count you.