Here is the update - I verified all again:
Plextor PX-716SA, Plextor PX-B310U, Asus BW-12S1-U
ImgBurn retrieves the ISRC from all drives
CUETools cannot read the ISRC from the PX-716SA
EAC cannot read ISRC data from the PX-B310U and is mixing INDEX times up (with that drive).
EAC is also messing up with these INDEXes with the Plextor PX-LB950.
So I guess that EAC and a Plextor BluRay drive is a bad combo for audio ripping.
Is this valid for other Liteon drives too?
I cannot verify anymore that EAC couldn't read ISRC from the ASUS. But I was pretty sure that EAC had problems. But perhaps it was only a CD with no data and when I checked a second time I tested only the B310U.
Is there a reason why some data which ImgBurn is showing us (like the ISRC data) are not for copying?