We discuss the origin of an enigmatic low-temperature behavior of one-dimensional decorated spin systems which was coined the pseudo-transition. Tracing out the decorated parts results in the standard Ising-chain model with temperature-dependent parameters and the unexpected low-temperature behavior of thermodynamic quantities and correlations of the decorated spin chains can be tracked down to the critical point of the standard Ising-chain model at ${sf H}=0$ and ${sf T}=0$. We illustrate this perspective using as examples the spin-1/2 Ising-XYZ diamond chain, the coupled spin-electron double-tetrahedral chain, and the spin-1/2 Ising-Heisenberg double-tetrahedral chain.