Breadman,
I can understand your confusion but I can also understand their position. They have to draw the line somewhere. If they extend the line for you because it's only 10 minutes then the next guy asks for the line to be extended because it's only 10 minutes past you and so on. It has to end somewhere.
Also, look at it from the drivers perspective. If he drops off the girl at your hotel and then goes to pick up a girl, takes her to another hotel and then returns to your hotel then the 10 minutes extra has turned into 40 minutes (10 min extra to drop her off, 10 min extra to get to the other girl, 10 min extra to return to your hotel to pick her up and 10 min extra to take her to her next appointment).
Agencies aren't the only ones that have to draw the line. I have a friend that lives 30km to the east of me and another that lives 30km to the west. When I call the friend to the west it's a local call but it's a long distance call to my friend to the east. It may seem arbitrary but that's the way it is.
I'm not sure this will make you feel any better but it may help explain why.