We prove that for d ≥ 3, the 1-skeleton of any (d-1)-dimensional doubly Cohen-Macaulay (abbreviated 2-CM) complex is generically d-rigid. This implies that Barnette's lower bound inequalities for boundary complexes of simplicial polytopes (Barnette, D. Isr. J. Math. 10:121-125, 1971; Barnette, D. Pac. J. Math. 46:349-354, 1973) hold for every 2-CM complex of dimension ≥ 2 (see Kalai, G. Invent. Math. 88:125-151, 1987). Moreover, the initial part (g 0,g 1,g 2) of the g-vector of a 2-CM complex (of dimension ≥ 3) is an M-sequence. It was conjectured by Björner and Swartz (J. Comb. Theory Ser. A 113:1305-1320, 2006) that the entire g-vector of a 2-CM complex is an M-sequence.