Charging, as nibot said, happens because the "balance of charge" is altered. If you have a neutral ISS, and you assume that no electrons are added or removed, the ISS will stay neutral. This can of course change, and the ISS can charge, if electrons are removed or added due to the exposure to ionizing radiations.
However, you are right to say that if a metal moves in a magnetic field, you obtain a charge separation, and consequently a voltage. The same concept is used in any dynamo to produce electricity. There was indeed an experiment using this concept:
It was deployed twice with little success, but it did produce a (small) voltage, and therefore create a current.