Randomex, that’s a good point, but I think it’s better to tell the Rav privately and let him decide if it was really a mistake and how he should go about correcting it, especially if it’s not an important mistake.
If it’s an important mistake and he has a way to correct it, but deliberately doesn’t do so, then you may be right.
In this case, it sounds like he had no way to correct it, and in any case, it wasn’t an important mistake (in the sense that it would not lead to someone to an incorrect hashkafa or halacha).