Shaun, maybe there is some confusion.. Did you connect the LiPo to a battery, battery charger or power supply?

Batteries are constant voltage - ie: they attempt to maintain a specific voltage independant of load.

Power supplies are constant voltage. I have a 300A 13.5V power supply on my test bench (amongst others) and it attempts to supply a constant voltage independant of load.

Battery chargers vary. The smarter RC chargers work on both Constant current and constant voltage. When you connect a battery, you set a charge current - 1, 2, 5 Amps or whatever. The charger attempts to maintain this current flow to put energy back into the battery as quickly as possible. Good quality chargers use Constant Voltage circuitry to monitor no-battery conditions... Without a battery connected, the device would attempt to produce infinite current as it attempted to push electronics into the air - overly dramatic explanantion... There is some addition adjustment of current at the end of the charge from an intelligent charger.

If you look at the display on the voltmeter attached to that battery, you can see that the voltage was changing as the internal resistance of the pack varied. Odds are, if you were monitoring current - it would have, assuming it was connected to a battery charger and not a power supply, stayed relatively constant.