Charging Issue!!

[Mustang_Driver]

My Brother has a 2007 Sonata 2.4l and tonight his wife had a hard time starting it so they phoned me and asked if i could load test the battery for them to see if it was the problem and my question is this:

Load test battery went to 11V and my weak light came on
Started the car it was charging at 13.3-13.7V
Turned headlights on,High Beams ON and heater to High the reading was 12.9V at idle

When i mentioned this to my brother all he said was well it's charging so can't be the alternator so he is going to buy a battery as that is what he says it is..

i say its the Alt or voltage regulator but as its a 2007 it is probably integrated in the ALT so does anyone have any thought as to who might be right

as i say running at idle 13.3-13.7 my ford van is 14.4-14.6 at idle i just don't want to see him waste his money on something that it isn't so any thought would be helpful