My DH has come running three times in 18 years of marriage and 15 years of parenting.
The first time was during my first pregnancy when I fainted while out in the city centre. I fell, hit my head and blacked out. When I came round and eventually was coherent a member of staff in the shop got my phone and called him. He ran to the car, drove to pick me up and took me straight to hospital to be checked out. If I hadn’t been pregnant, I would have just waited until I felt steady on my feet and then insisted on getting a taxi home. I think I freaked out the shop staff though and they were the ones who were pretty insistent with DH.
The second time I was also pregnant - 3rd pregnancy and pregnant with twins. I was at home with 2 other children (age 4 & 2) and fainted in the shower, hit my head, blacked out and threw up when I came round. I managed to crawl across the floor to my bed, get my phone and call him home. He called the midwife en route and she came too to check me over. Again, if I hadn’t been in a high risk pregnancy and if I wasn’t in sole charge of 2 small children I wouldn’t even have called him.
The third time was about a week after we moved into our new house overseas. I was in the house alone (DC all at school and DH at work) and I came into the living room to find a snake in the middle of the floor. I admit I freaked out. I stood stock still, called DH and didn’t move until he appeared. Luckily he worked walking distance from our house so he literally sprinted home and brought a local colleague with him. The colleague was much less freaked out than either DH or I and calmly informed us it was just a harmless garter snake, picked it up and tossed it in the garden. DH never lived in down in the office, but I was rather glad he came!
If I phoned DH and told him I felt unable to care for the the DC when they were young he would have come because he would know I would only call him in a genuine emergency. I have dealt with plenty worse than a stomach bug myself inc repeated fainting spells due to low BP and just got on with it. I’m an adult ffs! Like the vast majority of parents I’ve also dealt with injuries to the DC - split heads, split chins, broken bones, allergic reactions etc and just got on with it alone, with several other children in tow. That’s life!
I agree that they seem rather prone to over exaggeration and drama.