Electrophysiological measures of functional connectivity can be affected by the power bias, i.e., variations in their estimation due to variations in the signal-to-noise ratio (SNR) rather than in genuine neural interactions. Intrinsic functional networks emerge at rest from magnetoencephalography (MEG) amplitude connectivity mostly within the α and β frequency bands, where the SNR of MEG recordings is coincidentally maximal. This raises the question, is the spectral specificity of these networks really driven by neural oscillatory dynamics or is it an artifact due to the power bias? Here, we present a detailed theoretical analysis of the power bias in amplitude connectivity allowing to disentangle the neural part of connectivity from the nonlinear SNR dependence of estimated amplitude connectivity (as well as from the contribution of noise correlations). On this basis, we developed a new correction technique involving a SNR-dependent renormalization of amplitude connectivity, which we validated using synthetic data. We then applied the technique to resting-state MEG data and quantified to what extent the power bias affects the spectral content of intrinsic functional brain couplings. We demonstrated the absence of such effect, which was explained by the observation in synthetic data that the power bias is very reduced at the sufficiently high SNRs found in resting-state MEG recordings. Comparison with a classical linear regression technique highlights the importance of our nonlinear correction to reach this conclusion. Our analysis thus confirms the crucial role of neural oscillations for the spontaneous emergence of intrinsic brain functional networks.