I think this screenshot will illustrate what is going on.
Top waveform hits max digital level one bit per cycle. It is a max level 11,024 hz tone at 44.1 khz. Over time the phase of when samples occur vs the waveform slowly shifts. It is the same exact wave at the same exact level shifted in time in the bottom track. None of the bits are at max level. Now in the light blue area I've applied 2.44 db of gain which is allowed by this and most sound editors. It can cause two problems.
The middle track is upsampled to 352,800 hz sampling rate. It shows more closely the actual waaveform. As you can see the actual peak of the reconstructed waveform will be between samples and above the sample values. In the left side that would be fine, but in the right side it means the waveform is higher than what a zero level wave would be. If the analog section has this much headroom then fine no problem for the left half. For the right half already at near max levels upsampling will cause peaks to be above max digital level and the reconstructed upsampled waveform will be squared off. Like this one picture below. This was the bottom track above with 2.44 db gain upsampled to 352,800 hz sample rate.
So this waveform was a tone sampled in a place that left room for digital gain, but if upsampled it both would require headroom in the analog output, plus it would have pushed the digital values into clipping and you'd still get a clipped output waveform. Even with analog headroom.
Some noise like waveforms will require 10 db headroom to prevent this occurring. However they happen so rarely you likely wouldn't even hear the momentary clip even if such an uncommon noise-like signal occurred. So 3 or 4 db headroom can prevent this effectively from ever being audible.
Even then, this hardly ever matters. Modern retarded mastering means the waveforms are pushed way up and squared off even if not high enough to cause clipping. So they sound like clipping even if just hard limiting and high level compression.