Could you give me an explanation how it was possible to obtain a good snr and ber with a wrong constellation with good SNR and BER?
for BPSK the value of the bit is determined only by examining the sign of the real part. There will be errors only when the cluster of points approaches the imaginary axis, where the sign of the real point changes. If the frequency offset it small (it rotates slowly) and the SNR high, then for most rotations there will be negligible errors.
In practice you will probably have great difficulty tuning the receiver accurately enough for this to work. Furthermore, doppler shift in the channel may make the frequency change over time. Thus, the need for the Costas loop or some other frequency synchronization.