Police control

when from a country where police is usually absent, or only there to give you a ticket when you cross the red light on foot, or when your bike light just stopped working because of the rain, the police in the US, as mentioned before, can be rather frightening, yet at the same time ridiculous. this morning we left our perfect apartment and walked down the perfect path leading to the subway station (this path being especially constructed for our living community). arriving at the station, there were some policemen and a notice that people at random could be subject to "search" and that refusing this could lead to "arrest". the woman in front of me was picked, we luckily werent.
its good that i lunch with some real US citizens who explain me these kind of things. this is something the Transit Police can do, because as soon as you enter the railway station, you are on their property, and thus if they feel its necessary, they can force you to open your bag for example so that they can see whats in there. similarly, the harvard police can "search" everyone present in a Harvard building, if they feel to do so. but what if you then say: "ok, i do not want to be searched, i rather leave the building/subway station, this is ridiculous"? well, then you have a problem, because people who have nothing to hide, will not refuse such a thing, and they thus have a reason to arrest you.
i find that scary.... and not enhancing my safety. but maybe you will disagree with me on that...?