Given two pseudo-Riemannian manifolds \((B, g_B)\) and \((F, g_F)\), the product \(M = B\times F\) can be equipped with a metric \(g_M = f^2g_B \oplus b^2g_F\), where \(f, b:M\to\mathbb R\). Then, \((M, g_M)\) is called a double twisted product. If \(f = 1\), \((M, g_M)\) is just a twisted product. If moreover \(b = b_0\circ pr\), where \(b_0:B\to\mathbb R\) and \(pr:M\to B\) is the projection, then \((M, g_M)\) is a warped product. In this article, the authors show that twisted products with Ricci tensor vanishing on all pairs of vectors tangent to the factors \(F\) and \(B\) become warped products if only \(\dim F > 1\). Consequently, twisted products which are Einstein are warped (again if \(\dim F > 1\)).