Well, living in a “recently converted to democracy” country myself

, I am rather familiar with this kind of practice by road-police as the one you and Andrew are referring to.
On the other hand I had no idea that copies (laminated or not) are an acceptable alternative to original personal ID, driver license and vehicle registration documents. In what the passport is concerned, no citizen of a EU member state need to carry one in order to travel within the boundaries of the Union as the local ID card suffices. The passport is only necessary if one wants to travel (or even just cross) European states that are not members of the EU like Switzerland, former Yugoslavia states, Albania, Andorra, Iceland, Liechtenstein, Malta, Monaco, Norway and San Marino.
In what running away from the police is concerned, I don't see it as an option even less as a good idea, leaving behind copies of you papers or not.

In the case of Andrew's mate that was squeezed for bribery in Spain, he should have left his passport, taken the names of the officers and the registration number of the police vehicle they were in and left for the first police station in a larger city to report the incident (if he was indeed innocent of the offence he was charged with). Spain might be close to Africa, but is still an "old" EU member, and such crap should not be put up with...