first off, what are the odds of a woman ALONE in KSA??? They HAVE to have an escort,
and to take a ride from a strange man? That doesn't sound right.
Although this rule is in the books, and is enforced rather enthusiastically in other cities, Jeddah is the most liberal city in Saudi. Go anywhere around Jeddah and you will find women going around alone, taking taxis alone, doing their shopping, etc.
Jeddah has always been much more liberal than the rest of Saudi Arabia because of it's coastal location and a large number of foreigners living their. I think it was the last place to be conquered by King Abdul Aziz.
Going off-topic, atleast once every week in Jeddah you will see some youngsters beating up religous policemen and running away. If they are from a prominent tribe, the religious policeman will most likely be helpless and wont be able to do anything about it.