Model color-magnitude diagrams of low-metallicity globular clusters (GCs) usually show a deficit of hot evolved stars with respect to observations. We investigate quantitatively the impact of such modeling inaccuracies on the significance of star formation history reconstructions obtained from optical integrated spectra. To do so, we analyze the sample of spectra of galactic globular clusters of Schiavon et al. with STECKMAP (Ocvirk et al.), and the stellar population models of Vazdekis et al. and Bruzual & Charlot, and focus on the reconstructed stellar age distributions. First, we show that background/foreground contamination correlates with E(B − V ), which allows us to define a clean subsample of uncontaminated GCs, on the basis of an E(B − V ) filtering. We then identify a "confusion zone" where fake young bursts of star formation pop up in the star formation history although the observed population is genuinely old. These artifacts appear for 70%-100% of cases depending on the population model used, and contribute up to 12% of the light in the optical. Their correlation with the horizontal branch (HB) ratio indicates that the confusion is driven by HB morphology: red HB clusters are well fitted by old stellar population models while those with a blue HB require an additional hot component. The confusion zone extends over [Fe/H] = [−2, −1.2], although we lack the data to probe extreme high and low metallicity regimes. As a consequence, any young starburst superimposed on an old stellar population in this metallicity range could be regarded as a modeling artifact, if it weighs less than 12% of the optical light, and if no emission lines typical of an H ii region are present. This work also provides a practical method for constraining HB morphology from high signal to noise integrated light spectroscopy in the optical. This will allow post-asymptotic giant branch evolution studies in a range of environments and at distances where resolving stellar populations is impossible with current and planned telescopes.