So the important question is whether or not at least one of your batteries was selected when the engine was running.
Most likely yes, since he was able to start the engine.
To test your charging system, select ALL on your battery selector (if you have one - not all boats do), disconnect the shore power and fire up the engine. Take a volt meter (a cheapie from Radio Shack will do fine) and measure the voltage. Just put the black test lead on either battery negative terminal and the red one on the same battery's positive terminal. Make sure the meter (1) is set to measure DC volts and (2) that you have it on a scale that is more than 14 volts (most have scales that max pout at 10 volts, then another at 50).
You want to see 14 volts DC or slightly more. If you are not sure how to read the meter, note where the needle is and shut the engine down. The needle should move down a bit, to 12 or so volts.
If you see no change in voltage with and without the engine running, you probably have a charging system problem. If you see a very high voltage with the engine running, you probably have a problem, in this case a damaged voltage regulator.
From what you described though I think thr odds are high that you're fine. Of course I don't know how your boat is wired but I am playing the odds.