No drive can transform a low quality disc into a good disc. Some drives are more picky than other, and probably the Asus it is really picky, but the culprit in your case is still the disc.
To be sure that you got a defective drive, a successfully burn of these discs on a benq drive is not a reliable test. Try to burn some proven quality discs on the asus: if you still get power calibration errors, then there is really something wrong. It could be a faulty drive, a damaged cable, or an insufficient PSU.
As I already said, the previously successful burnings with that media are not an evidence that the drive has something wrong: there is too much variability in low quality discs so probably in past you got a decent production batch and this explain why you were able to burn these discs successfully.