To see this, let us consider the Anderson impurity model which consists of one impurity orbital and n bath bath orbitals. The model allows only single excitations and only between the impurity and the bath orbitals, i.e. there may not be any excitations between bath orbitals. If we start from a determinant, where the impurity is doubly occupied and select a particle on a bath orbital to excite from, there will be no valid single excitation possible.