A sample-safe file can still exceed a true-peak ceiling between samples.
Peak normalisation aligns one extreme value; loudness normalisation aligns an integrated programme measurement.
A delivery specification should name dBFS, dBTP or LUFS rather than saying only “normalise the audio.”
The full explanation
Sample peak, true peak and programme loudness describe different properties of digital audio. Sample peak checks the values actually stored in a file; true peak estimates the continuous waveform between them; loudness applies a time- and frequency-aware model. Choosing a gain safely starts by naming the measurement the delivery target actually requires. Read the complete guide for the reasoning, examples and definitions behind this answer.