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We present data on charged kaons (K±) and ϕ mesons in Au(1.23A GeV)+Au collisions. It is the first simultaneous measurement of K− and ϕ mesons in central heavy-ion collisions below a kinetic beam energy of 10A GeV. The ϕ/K− multiplicity ratio is found to be surprisingly high with a value of 0.52±0.16 and shows no dependence on the centrality of the collision. Consequently, the different slopes of the K+ and K− transverse-mass spectra can be explained solely by feed-down, which substantially softens the spectra of K− mesons. Hence, in contrast to the commonly adapted argumentation in literature, the different slopes do not necessarily imply diverging freeze-out temperatures of K+ and K− mesons caused by different couplings to baryons.