They're thinking about when you sample from the same noise distribution, averaging gives an unbiased estimator of the mean. But when you know one SNR is higher than the other, maybe this doesn't hold? But maybe if you transform the distributions to look the same, thus taking a weighted average? I'm not sure.
It does hold, it is just weaker. You can improve the SNR of a better signal by adding another signal with worse SNR to it. But you need to normalize the signals the way their noise floors are the same amplitude before addition.
Signal0: infinite SNR. Signal1: anything less.
I just don't see how the output of averaging these would improve over Signal0. I don't think it can.