propensity matching and ITT for cohort study

I am reviewing a cohort study that used a retrospective database to determine if treatment with hypothermia post cardiac arrest improves survival to discharge. They used what seems like fairly robust propensity matching analysis. However they then adjusted afterwards again with sensitivity analysis and excluded all patients who died within the first 24 hours. Justified by saying that this should in fact show favour for the intervention of hypothermia in survival data, assuming sicker patients were more likely to receive the intervention and therefore more likely to die earlier so this should remove any indication bias.
Should not all patients have been kept and analysed on an intention to treat basis? Also, as a clinician my experience is that the sicker patients don't get the intervention as they cant tolerate it. It is meant to be a treatment based on neurological status regardless of "level of sickness". Am I right in then thinking that this could then introduce MORE bias risk and in fact benefit the control group or does the propensity matching done prior balance enough that it shouldn't impact the results?