I read a recent review of a camera which can use either its mechanical shutter or an electronic shutter. The review mentions a problem they noticed with the mechanical shutter, and then notes that the problem "can be eliminated by switching to electronic shutter mode, though this comes with a slight cost to dynamic range and a risk of rolling shutter."
I understand the rolling shutter issue, but am curious as to how the electronic shutter might affect dynamic range. Several answers to Why don't they make all DSLRs with an electronic shutter? suggest that this is because of the sensor construction required to enable such a shutter. But that doesn't make sense in this context — if it were a limitation due to construction, the dynamic range would be reduced even if that part is switched off and the mechanical shutter used instead.
So, what's going on here? Is the review simply carrying the knowledge that electronic shutters increase noise without understanding the details, or is there some other reason electronic shutters increase noise?