If we observe the so called Pioneer anomaly as an unexpected
constant Doppler blue-shift drift, then we should expect a constant
Doppler red-shift drift, if the experiment were performed from a
Pioneer probe as the base reference and the Earth were the target.
From that point of view, we'd wrongly conclude that the Earth is not
where it should be. IOW, we would observe the Earth from a Pioneer
probe as orbitally decaying toward the Sun. Should we conclude then
that the Earth is radiating gravitational waves?