What you said is only true for organisms which happen to engage in haplodiploidy. From the paper by Nowak et al in the OP:
By the 1990s, however, the haplodiploid hypothesis began to fail. The termites had never fitted this model of explanation. Then more eusocial species were discovered that use diplodiploid rather than haplodiploid sex determination. They included a species of platypodid ambrosia beetles, several independent lines of Synalpheus sponge-dwelling shrimp (Fig. 2) and bathyergid mole rats. The association between haplodiploidy and eusociality fell below statistical significance. As a result the haplodiploid hypothesis was in time abandoned by researchers on social insects
What you said is only true for organisms which happen to engage in haplodiploidy. From the paper by Nowak et al in the OP: