A common misconception. The bird is primarily IRS derived but also has a static input. See below from the FCTM (my bold).
FCTM > Aircraft systems > Bird
RELIABILITY
The bird is computed from IRS data and is affected by inertial errors. During the approach, the flight crew may detect a small track error, usually up to +/-2 °.
The bird is also computed from static pressure information. Therefore, if the altitude information is not reliable, the flight crew must consider the bird as not reliable.