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It was demonstrated in a series of papers employing unitarized chiral perturbation theory that the phenomenology of the scalar open-charm state, the $D_0^*(2300)$, can be understood as the interplay of two poles, corresponding to two scalar-isospin doublet states with different SU(3) flavor content. Within this formalism the lightest open charm positive parity states emerge as being dynamically generated from the scattering of the Goldstone-boson octet off $D$ mesons, a picture that at the same time solves various problems that the experimental observations posed. However, in recent lattice studies of $Dπ$ scattering at different pion masses only one pole was reported in the $D_0^*$ channel, while it was not possible to extract reliable parameters of a second pole from the lattice data. In this paper we demonstrate how this seeming contradiction can be understood and that imposing SU(3) constraints on the fitting amplitudes allows one to extract information on the second pole from the lattice data with minimal bias. The results may also be regarded as a showcase how approximate symmetries can be imposed in the $K$-matrix formalism to reduce the number of parameters.