No, I think that's not a paraphrase of what the Buddha said.
Instead the Buddha is famously reputed to have said that there is rebirth.
For example, the following are examples of suttas in which he talks as if he had direct (supernatural) knowledge of rebirth.
When teaching the path to awakening to others, he defined the four stages of awakening achieved by the path in terms of how many rebirths remained for those who reached them: up to seven for those reaching the first stage; one return to the human world for those reaching the second; rebirth followed by total liberation in the Pure Abodes for those reaching the third; and no rebirth for those reaching the fourth (AN 3.86). On occasion, when one of his disciples who had not reached full awakening passed away, he would comment on the disciple's rebirth — as when Anathapindika the householder, after his passing, appeared to the Buddha as a heavenly being (MN 143). When any of the Buddha's fully awakened disciples passed away, he would state that one of the amazing features of their passing was that their consciousness could no longer be found in the cosmos. Rebirth, he said, happened to those who still had clinging, but not to those who didn't (SN 44.9). And one of his own amazing attainments as Buddha, he said, was that after the end of this life, the world would see him no more (DN 1).
When discussing more mundane topics, such as the rewards of generosity and virtue, he would cite the rewards they brought not only in this life but also in future ones. Even in cases where he was asked specifically to confine his discussion to the present life, he would end the discussion by referring to the rewards of these skillful actions after death (AN 5.34; AN 7.54).