[ossiblue]

Hopefully, Superman's suggestion will solve the problem but it's a bit of a puzzle. Since you say the problem happens at any hot water faucet, that means air must be entering the system an a point common to all--water heater is a likely spot. However, for air to enter, there needs to be a breach somewhere in the pressurized circuit and that means water should be leaking out when the hot circuit is "off." You checked the meter but a small leak may not be detected by your test method, depending on how long you had everything turned off. If you are on a slab foundation, the leak may be under the slab.

If you don't remedy the problem by tightening the connections at the heater, you may wish to call out the water company or an plumber to electronically look for a leak. Not fun but may be your only peace of mind if you can't fix it at the heater. Regardless, please let us know the results as this is a problem that we all may face some day. Good luck.

edit: One possibility may be the pressure relief valve. It may be holding pressure when the hot water is "off" but when the hot is turned "on" and pressure is reduced inside the tank, the valve seal may open slightly and allow air to be sucked into the top of the tank where it passes into the system. Never heard of that happening but it seems possible and it is something to check before you go to the expense and worry of tracking down a leak in the pipes.