Wade's rules (and related skeletal electron pair counting methods) are successfully used to interpret and rationalize the structures of Zintl ions.
Paper 1 discusses Wade's rules in relation to Zintl clusters and deltahedral boron hydrides, showing how skeletal electron counts apply. Paper 4 explicitly uses Wade's rules to interpret the bonding in a Zintl crystal structure. The other papers are either about different types of complexes or general definitions and do not contradict the claim.