Hi ankerdine, I think you have guessed right, in that the midwife / friend / relative had have stayed there.
On my fathers side I always wondered why my great grandmother gave birth to one of her sons in Greenock (they lived in Anderson Glasgow, I found out that her sister when she married moved from the family home at Cardross over the Clyde to Greenock, so she went there to give birth with her mother and sisters around to help.