But again, since they neglect to mention overcharging,
What do you mean by 'overcharging' ?
All caps will charge to match the applied voltage across their terminals and then current ceases to flow because cap and charging voltage are equal. If you try and 'overcharge' by increasing the charging voltage above the max working voltage rating then you will indeed destroy the capacitor. As long as the one stays within the voltage rating of the cap it's not possible to overcharge it. Now if you mean charging current rate density, then again we are back to the internal resistance of the cap that will limit the charging current rate per ohms law.
I mean "overcurrenting", it's just that that's not actually a word.
And again, since supercaps are inherently very different than electrostatic or electrolytic caps, I imagine they might have different electrical tolerances than the other kinds. I understand that you really can't charge a normal cap too fast, but these things are designed for low, low current draw, which is why I have my doubts.