When open circuit (i.e., the generator wires are not hooked to a battery, you are just measuring them), those generators put out voltage pulses and even if the peak of the voltage pulse is over 12 volts, when you test it with a simple DC volt meter, the meter doesn’t see the peak, only some sort of average. So even if the meter shows 6 volts, you still can have peak voltage pulses higher than 12 volts and charging the battery. The DVM does some sort of averaging so reads a much lower voltage. Try the same test with a scope..
However.. I think those old Honda's were pretty susceptible to having the rectifier blown by disconnecting the outboard charge wires from the battery while the outboard is running. I had a 1990 Honda BF8 and when I bought it, it had the rectifier blown. No complaining about the PO in my case (who put a great traveler on the boat) but there was a switch between the battery and the outboard charger on the boat. The switch would have been OK if you ONLY change the switch with the outboard NOT running but open the switch while the outboard is running - ZAP.. blown rectifier.
I sold that Honda BF8 but it was still reliable and had a lot of miles on it.
For the OP, if you are considering fixing the charging circuit, you might check what a new rectifier costs and if you do fix it, never disconnect the battery while the outboard is running. I had fixed the rectifier on mine but the charging circuit on the 2010 Nissan 9.8 that I replaced it with works way better so Im not sure I would fix it again if I still had the old Honda.