Fixtures will not run hot water unless another fixture is on
No other fixtures are "dependent" on the shower valve. What may be happening is what is called "crossover", hot water crossing over into the cold water line (or vise-versa) due to a defective single-handle mixing control. It sounds like your plumber may have been right, as this would tend to not have a noticeable effect when the shower is flowing. When the shower is static, you turn the hot on at a different faucet, cold water is pulled through the defective shower cartridge to mix with the hot in the supply line, resulting in luke warm water. 

Troubleshoot by positively shutting water supply to the hot water side of your system and checking for flow at a hot water tap, or have a plumber replace the shower mixing valve