Since all flood forms share memories, knowledge and thoughts.(wiki+gravemind quotes) And since the first gravemind was more or less a Precursor(wiki+books). Then the gravemind speaking to us in halo 2 and 3 is technically a precursor. You would say it is only 0000000.1% precursor since the rest of the memories are other species but remember that the precursors created the flood and the first gravemind. So it's safe to say that their indentity prevails over the rest. The flood are , after all the Precursor's creation.