Short answer: yes.
Realistic answer: it can be dreadfully complicated.
In the ED where I work, there are many, many moving parts in a metaphorical fast, fluid dance. Computer systems: Pertinent patient medical history for most patients, including clinics/doctors/implanted device serial numbers, meds, past workups (both conclusive and inconclusive), etc. Very useful almost all the time, can get by if the patient is a good enough historian. I suppose there is a way to get paper-based printouts in a no-computer situation, but I am not familiar with it (all our system downtime where I work falls back to a read-only system, not a no-access system). Our systems also coordinate imaging/lab orders. Yes we can fax paper orders, call, and face-to-face with our teammates in different parts of the building -- but the higher the census/acuity, the more chaotic it is when we are not practiced with that method, and mistakes are much more likely to happen. Meds/procedures are also ordered and communicated on the system, and completion/administration is charted on the same. Patient exams too. Notes. Pertinent allergies or history the patient forgot to tell the doctor but told his/her nurse afterwards (then it is entered right there so when a certain med is ordered, a flag is raised to everyone who needs to see it). We are very, very used to being able to communicate centrally like that. Going to temporary paper charts is doable - just much slower. As we don't do it everyday, everytime we need to re-rehearse the system. Our rapid, fluid dance crashes and we're fumbling almost blindfolded, trying to get the same amount done/communicated/verified/double verified with our same patient load as before.

Real life example: during a (seemingly) poorly-planned downtime of our charting system (maintenance), we got several simultaneous critical trauma patients involved in more than one unrelated MVA. As they arrived very close to each other, they went to CT for imaging as soon as primary/secondary evaluation was done. As there was more than one CT available, 2 went simultaneously. None of these patients were conscious and therefore couldn't verify their own identity. In the hurry to evaluate and stabilize them, two of them had their namebands switched (the namebands didn't use their actual names, just random computer-generated and obviously not belonging to a real person type names, for the sake of brevity (no time to hunt for IDs or make calls yet) so CT/labs/everything else can happen ASAP). Quite fortunately the error was found after the scans were completed but well before the neurosurgeon came to evaluate and do a life-prolonging invasive procedure the wrong (intubated trauma) patient. This seems like a simple thing to prevent, and it is, provided everyone remember to slow down and be mindful of these steps.

Now I imagine the ED at that hospital at capacity with high acuity patients with a very full waiting room (as flow has slowed down considerably), and perhaps a decision was made to go on divert (EMS directed to take all incoming patients to the next closest appropriate hospital). If the physicians and nurses (and all other staff that keep the place from sinking into the mud at any given time) were all occupied with critical patients at the time this patient was to arrive, my experience tells me that there would likely be a high risk that somebody was going to have a bad outcome because the demand exceeded the resources.
This is just my take on the situation given almost no data other than that computer systems were down and this patient was diverted to another hospital and died. I don't know the emergent medical condition nor do I know if it was due to lack of timely hospital resources that she passed. What I do know is that if that ED was at its max with critical patients (and metaphorically raining fire and brimstone sent from the vengeful ED gods because a non-superstitious staff person remarked how "quiet" it was that shift and superstitious coworkers became upset), she may not have had a good chance there either, or somebody already there may not have had a good chance. Who knows. I can only speculate.