I've had some DC 12v batteries than when fully charged and rested would read 12.8v
I've had others that would read 12.6v under the same circumstance.
I have an AGM battery that reads 13.07 volts when rested and fully charged.
These " universal" Voltage charts that proclaim states of charge are amusing, especially when it is not pointed out that these are rested voltages, not voltages under load.
Now if the voltage/SOC chart was given out by the battery manufacturer for their specific battery, I would put more stock in them, but I would not put any stock in them unless the battery had not seen any charging or discharging source for many hours, unless I had been monitoring them for many many cycles while discharging them in a similar manner.
If someone sees 12.02 volts under a 5 amp load and freaks out cause such and such a chart says it is in the danger zone, well I guess the only damage done is on the person who freaks out and starts recharging prematurely, and this can only be a good thing for the battery, so no harm done.
Unless you fire up your generator next to me.