edr2694:
I'm not entirely sure how the analog pins could be "back powering" anything
Back-powering is when current finds a path through the protection diodes on the pins to the ATmega's VCC and effectively allows the chip to be powered even though now voltage is present at the VCC pin(s).
It is most common when people are using the analog pins to measure the voltage of a battery. In most cases the battery is separate from the supply used to power the ATmega / Arduino board. Since the grounds are connected together, there is a path for current to sneak through the ATmega chip when the chip's supply is removed.
The result is strange behavior like the chip being powered even though VCC is removed, strange start-up behavior and strange latching behaviors. Analog readings of 300 are pretty close to 1.4V, which is awfully close to two diode drops...
Sound familiar?
edr2694:
I'm not sure how a Vcc would make a difference unless a voltage greater than it was input
When VCC is removed, you're changing the entire circuit. In this case, the bias on the protection diodes change.
edr2694:
The ground plane is the same, so the values at the pin should be no different than what it would be from any other analog sensor.
Sensors don't provide (relatively) large amount of current. If the sensors are powered by the same VCC as the ATmega, they don't really do much of anything when it's VCC is removed.
Voltage dividers connected to batteries do, however, have a nice supply of current available.
edr2694:
It's weird that I only ever saw this behavior on one of the two MEGA's I have with the exact same setup.
Manufacturing differences in the chips will lead to slightly different behaviors. Things like the pull-up resistors and protection diodes don't have tight tolerances. This leads to slightly different behaviors, which are technically still within spec (by not being tightly specified).