My FIL has a chronic illness that sometimes renders him incohent and agitated for days. Because this is a very rare illness, the ER doctors typically assume he's having a heart attack and treat him acordingly. Really, he just needs time to get over these spells and he'll be fine. So he's given his family strict orders - do not call 911 when he's having an episode.
A few years ago, he was having an episode. He told his wife - no 911. A couple of days later, he was worse. The kids thought maybe he should go to a hospital. His wife said no, he had told her no 911 calls. A couple days later, he tried to get up to use the restroom and fell over. MIL called my husband, who went over there and decided to go against dad's orders and call 911.
It turns out that it wasn't an episode. It was a major brain bleed that was pushing his brain against his skull and almost killing him.
I know this is anectdotal evidence, but making the wrong call (no pun intended) can be deadly.