The problem is that not all nursing homes are staffed by skilled nurses who care about their patients and can determine when there is a true emergency. Or the staff may not be quite as bad as that, but having so many patients to tend to, they might not be able to pay as much attention to one particular patient as might be needed; so, you might have a situation where a patient has a minor emergency that doesn't warrant calling 911, so they call a private company, but meanwhile, while the private company is on its way, the patient gets worse gradually, which is not noticed by staff.
I was recently called to a particular nursing home for a patient whose chief complaint, according to the staff, was "general lethargy and decreased appetite". (Another common nursing home patient complaint like that is "failure to thrive".) Anyway, I get there and do an assessment; pt. has recently (according to staff) altered mental status and is unable to communicate, and a BP of 72/38. Here's someone that clearly should have been at the hospital already, and probably could have been there quite a bit earlier had they called 911. But the staff based their decision to call us on factors other than BP, which at the last regular twice-daily check was 100/50. So either they weren't monitoring the BP more frequently because it wasn't a problem at the last regular check, or nobody cared enough, or knew enough... Anyway, we didn't run that one L/S, nor request an ALS rendezvous, because that NH happens to be next door to the hospital, so no point.
I'm sure it's the same all over, but some of the nursing homes around here are really quite deplorable, and it's amazing people ever get out of them alive.