Yes, a vacuum breaker is a type of check valve; when pressure in the WH is less than outside it opens and lets air in. When WH pressure goes positive (greater than outside the tank) it shuts. Do you have a check valve on the cold water lines near where the lines enter the WHs? A check valve at this location would prevent cold water running elsewhere to depressurize the WH (provided the check valve holds). Also, maybe Larry will input; I think he recommends spring check valves vs. swing check valves.
And even if you did not have check valves at the WHs, if the VBs were working, you should not have had a problem. If the VBs worked and you did draw a vacuum and ran water a long time, you could draw enough air into the WH to expose the top element. Then it could dry fire.