Hello Sophie:
Both approaches are correct because linear regression applies a linear transform to the sensor data, and source projection is just another linear transform. That said, the source projection linear kernel is optimized (in terms of SNR) for sensor data. It is hard to predict what would be the effect of applying it on beta coefficients, which in essence correspond to a higher-SNR (filtered) version of the data: It might actually do what you describe, which is an overestimation of the SNR wrt what is actually present in the sensor data.
Hope this clarifies a bit?