This has been my experience in the U.S. It is a problem if one has locked the bag since it may be difficult to unlock the bag without touching it.

OTOH, in a recent departure from ZRH, where screening is run by the Kantonalpolizei, the screener asked me to open my own bag, find the object that she needed to examine (it was a corkscrew with a small knife blade), and then remove it from its retail package. The practice there is to rescreen any bag that has had to be opened; she carried it back to the x-ray and then brought it to me.

Another surprise: the next passenger had several bottles of liquids that weren't in his 3-1-1 bag. The screener sorted through everything, determined that some items that were in the 3-1-1 bag didn't need to be, and repacked it all so that the actual liquids were in the bag, all the while explaining politely (in Swiss German, which I understand only partly) why some of the things didn't need to be in the bag.