The original question to which I responded referenced Texas law, so the answer to that would be yes.
Of course. Anything mandated by state law would be reflected by explicit written hospital policy.
Doctors declared death and time of death. Notice to ME was usually made by Nursing Supervisor.
By phone.
I was a staff RN and shift charge nurse. I was not a unit manager or nursing supervisor, so I can't speak to their documentation. We (nurses) would be notified that it was a ME case or not (affected post mortem care; for example, a patient going for autopsy left with all tubes in place-ET tubes, central lines, etc., whereas a patient going to a funeral home had everything disconnected, was cleaned up, etc.), that kind of thing. I would always document my post mortem actions, so by reading my notes, it would be obvious if my patient was an ME case. As a staff RN, I never spoke to the ME so can't speak to how they responded.
Speaking only for my working experience (ICU in a county hospital, ICU in a large metropolitan hospital) and not for every medical facility in Texas, absolutely NOT. Never would a requirement to call the ME in the case of a death occurring within 24 hours of admission "slip through the cracks." NEVER. The facilities in which I worked took state law pretty seriously. ICUs are well acquainted with death and the laws which pertain to that. Roles were well defined with respect to this kind of thing. If you are asking if medical facilities do not comply with the mandate to report a death 24 hours after admission, all I can say is that in the facilities where I have worked, that would never be the case. I personally have never worked in a facility where the staff was "overworked and underpaid" to the point where they would neglect to follow state mandates, either willfully or by neglect due to distraction. In fact, I'm happy to say that every unit in which I have worked has always been run completely "by the book" in every way; that ethic was something I always perceived to have come from the top levels of management all the way down to the staff nurse actually providing the care. In my experience, anyone who didn't have pretty high standards for themselves didn't last very long in our environment. Even if one didn't have a strong work ethic, most professionals in this kind of environment are acutely aware that the potential for litigation provides the wise professional with plenty of incentive to cross all one's T's and dot every i. Other nurses may have different experiences.
As to the Munoz case, I have no knowledge whatsoever of the timeline of anything related to her condition or care.
