Recently, it was noted that absorptive corrections to the electromagnetic form factor in highenergy proton-proton scattering are important for the theoretical interpretation of the p ↑ p and p ↑ A analyzing power AN(t) measurements with the Hydrogen Jet Target polarimeter (HJET) at RHIC. Here, a concise expression for the absorptive correction was derived within the eikonal approach. The resulting analysis reveals a systematic bias, nearly independent of the beam energy, in the experimental determination of the real-to-imaginary ratio ρ when absorption effects are overlooked in the data analysis. Quantification of this bias, as ρ meas = ρ+(0.036±0.016) bias , was achieved using a Regge fit applied to available proton-proton measurements of ρ meas (s) and σ meas tot (s). Considering the potential impact of such an effect on the experimentally determined AN(t), one may enhance consistency between the HJET and STAR measurements of the hadronic spin-flip amplitude. While the sign of the bias in the value of ρ aligns with the anticipated effective increase in the proton charge radius in pp scattering due to absorption, it amplifies the observed discrepancy between σ meas tot and ρ meas values at √ s = 13 TeV as measured in the TOTEM experiment. Evaluation (using published TOTEM data) of the measured proton-proton dσ/dt dependence on the absorptive corrections indicated that possible soft photon corrections to the hadronic amplitude slope may be essential for such data analysis.