Cold water entering hot water circuit?
The only time I ran into something similar it was due to a failed anti-sweat mixing valve on a toilet that allowed back-flow through the hot water pipes. That would also explain in your case why the kitchen sink doesn't seem to be effected by the issue. 



About the only way I can think of to test this theory (without opening walls) would be if you can cut your cold water off to the bathrooms without cutting the supply to the hot water heater. In the unlikely event that you can do that, your toilets would still be able to fill from the hot water line when flushed.