Agree there should not be any problem running alternator a battery charger at the same time. If something bad happens, probably a result of a fault that already existed and they should be happy it happened at the dock!
About chargers: Anyone using a cheap auto charger should stop immediately. Those things are not ignition protected, and they may contribute significantly to galvanic corrosion, and worst case may cause stray voltage to enter the water via DC ground and hurt possibly kill someone. This is due to the fact that they may not use an isolation type transformer. So there are 3 reasons why using a cheap automotive charger may screw up someone else's boat, and I know there are a bunch of you doing it!!! arrrggg.
So.. trickle charging good or bad?? I have always left my 10amp double bank guest charger on at the dock, never noticed any significant loss of water from the batts. Going 2 years now and I haven't noticed any loss of capacity.