It is a complete falsehood that the only person you know for certain is the president, each and every citizen has some kind of identification. You argument can hold true for any other country in the world.
It is not true that all policemen are criminals in borrowed uniforms, there are lots of honest hardworking men and women that do their work with dignity each and every day. You will find directing the traffic, investigating crimes and other jobs. This is not to say there aren’t some bad guys, read here,
http://www.angelfire.com/ny2/bluewall/main.html?police. Also read
http://en.wikipedia.org/wiki/NYPD, “difficulties” would this lead you conclude that the entire NYPD is corrupt. No, that will be insulting the thousands of honest and upstanding men and women that put in their best each and everyday
Since you insist on facts, it is not factual that the Nigerian customs are a bastion of corruption. They are, just like in the earlier example good guys and bad guys.
Now to how do you make it there, now matter where in the world you are there is a Nigerian Embassy or Consulate, contact them for information and they will provide you credible contacts for any purpose that you choose.