This is an interesting question that I have never really considered. Does the Phantom start out assuming it is @ 0', or does it attempt to ascertain your actual altitude above sea level? I am unsure of the answer? My bird never shows 0' upon power up, and usually displays in the 3-15' range'. In my typical flight locations those would be expected & accurate ASL readings.
From a simplicity point-of-view, it makes sense to simply initialize the pressure sensor on power up, and display this point as 0'. The effect of variances in local atmospheric pressure would be minimal flight to flight, and no calibration would be necessary.
The bird cannot rely soley on the internal pressure sensor, as this is affected by atmospheric pressure conditions and requires calibration. Most devices with a barometer, a Garmin Vista for example, have a means for calibrating the barometer. No such means exists for the Phantom.
Using GPS-based altitude readings for determining initial altitude would result in wild variations in accuracy depending on the amount of clear sky surrounding the aircraft. If I recall correctly, GPS-based altitude readings suffer approximately 1.5x the error of horizontal positioning. The discrepancy can be quite high...75' or more!
I am curious about this now and will pay closer attention over my next flights. It will be difficult for me to judge as I am so close to actual sea level. I wonder what those who live at higher elevations see when initializing?