I don't doubt that at all but would love to see the evidence! I'm wondering how they show that, maybe DNA sequencing of T-cell receptor sequence? Or is it only through reactivity if specific proteins? Off to search about T-cell repertoire data...
Aha, I think you may have been in error in your post, then.
Vaccines can be targeted to many different parts of a virus, usually different parts of the surface protein. Different vaccines for the same virus may result in entirely different antibodies.
Even the same vaccine may result in different antibodies in different people. The process of antibody creation is random, and involves recombination of specific DNA chunks. And it's different in T cells and B cells.
So to say that the vaccine and the disease generate the same antibodies has meaning, but it needs to be shown by evaluating the specific protein sequences (most likely by sequencing the DNA or RNA that creates the antibody).