When giving birth? If the woman is actually giving birth at that moment, she is not going to be driving anywhere. With that precipitous of a labor, she (or someone with her) would likely call an ambulance to be transfered AFTER baby arrived, but even if the amulance arrived before the baby, the paramedics would not be trying to bundle her onto a gurney while baby is emerging. They would catch the baby, check it and mama over, and THEN transfer both of them.
If you are talking about labor -- there is rarely any need to use an ambulance for this. Labor is not a medical emergency, the woman doesn't need any particular medical care during the drive, and it's not like the paramedics are going to give her an epidural so she doesn't 'suffer through the drive.'
The only rational reason a woman MIGHT call an ambulance is if things DO seem to be progressing so fast that she thinks it unlikely that she would make it to the hospital in time, or she has absolutely nobody to drive her. (It's not advisable to drive yourself to the hospital when in active labor.) And both of these are rare situations in the U.S. anyway.