No, that would be double hearsay, hearsay within hearsay. The first example--Jane told me she was speeding--is hearsay.
It depends on the purpose of the testimony. If John Doe testifies Jane said she was speeding, it is direct testimony to what Jane told John. It is hearsay evidence to Jane actually speeding.
Florida law allows direct testimony to the patient's EXPRESSED wishes. If Michael Schiavo was testifying to what Terri told Michael, it is direct testimony to their conversation.
I am not saying Michael is testifying truthfully, just arguing what type of testimony he gave.