Regardless, the point is that it's somewhat disputed and not clear from Revelation when the soul actually leaves the body at death, so the rule of thumb is that it's permitted to perform Last Rites conditionally until rigor mortis (i.e. putrefaction). I think rigor mortis was set up as a more obvious criterion that can be easily tested, since without lab tests it's hard to know when putrefaction has begin.
I comment here as I work for a funeral home, albeit as an unlicensed assistant. My degree was in Animal Science (which did involve some training about and experience with biological systems and deceased matter) rather than Mortuary Science.
Rigor mortis and
putrefaction are different phenomena and have a distinct order in the post-mortem process (ref.
https://en.wikipedia.org/wiki/Putrefaction ). They also occur a few or several days apart. The timing of when the different stages postmortem appear can be affected by environmental conditions, the condition of parts of the body premortem (poor circulation for example), and any trauma associated with death. In my experience it is usually not that difficult to determine when
putrefaction has begun and we always hope to bring a deceased into our professional care before it does.