Plot hole

As much as I've enjoyed this movie over the years — and I've seen it several times — there's one hole I just can't ignore:

Even in 1984, no one would have got into a car with a stranger the way Alex did at the start of the picture!

Granted, without that bit of business they'd not have had a movie; but how do you bypass that or get around it or ignore it?

I remember when Cleopatra went to the Temple of Ra to lead a few cheers.