If you get a pass through using a 125 gr in a 30-06 for deer, it must be a close shot or the deer are not that big in the body.
Bullet construction is far more important than bullet weight.You would have a better chance of a pass through with a 130gr ttsx or tsx than with many 165gr bullets.
By the way,it's more likely that you will get a pass through with a longer shot than a shorter range shot,because the bullet is traveling slower at longer ranges,and will expand less as a result.