It explains that in a digital camera sensor, the amplifications/gains have to be turned up to increase signal/iso to create set iso values according to standards set forth. So the only way to increase gains/amplify signal in electronics, voltage would have to increase. Now we are talking mV more then likely sense cameras run on such small batteries.
The D800 has a 7.0V battery rated at 1.90Ah. You can put 8 AA batteries rated at 1.2v each with 2.00+Ah in a battery grip equal to ~9.6v and ~16.00Ah+/- off rechargeables..... Still not a lot off voltage.
Say on a D800, each base iso pic uses a burst of 500mV, then iso 200 uses 525mV, iso 400 could be 550mV, etc. and say iso 6400 is at 650mV, these small increases will use more battery power. Small increases, but can add up though.
Got a little technical but hope it helps explain why I would say higher iso's can create higher draw on a battery.