In the first level of dream, Robert Fischer took a taxi cab driven by Arthur. Robert Fischer is a billionaire. So why didn't he have his own limousine? And shouldn't there be private security for him?
It was a dream, and the architect made a scene where he doesn't have his own car (a foreign city). Private security was all around in the dream and they did attack the intruders right away.
The sequence of events is key here. At the beginning of the dream Fischer finds himself at the train station. He's got a lot on his mind (his father is very unwell) and he's not entirely sure how he got there but he clearly recognises that there's little point hanging around the station when he's an important man with a business empire to run.
He goes outside to hail a cab and luckily for him (and despite the rain) a cab instantly lights its "for hire" sign and he jumps in.
As far as "private (dream) security" is concerned, they don't kick in until his subconscious starts to notice that he's not dreaming his own dream, at which point a veritable trainload of security personnel arrive.
You may also note that he doesn't travel with bodyguards when he's on the plane, so perhaps he's not that interested in having security people around him.