Yes. More often than not it's due to the headgaskets having already been replaced, cheap gaskets, poor quality job, etc, or someone limping them around with low coolant/other issues because the cars are getting older and lower value, hence more prone to poor maintenance, ignoring issues like coolant loss, etc. Failure modes expand once the heads are off and gaskets replaced.
You're right, it would just be more accurate to say it this way: