Sylvan, you are right about that. One wonders why anyone would install a check valve, or other devices like a pressure reducing valve or backflow preventer on a plumbing system without installing an expansion tank on the ‘pressure vessel’ side of it. After all, when you put a backflow preventer on a plumbing system, therefore isolating it from the water mains, you are making the entire system a pressure vessel. To do so without giving the water someplace to expand, you are just asking for excessive pressure in that system.
Although there is some air in the incoming water (about 5% by volume) and the water will expand about 3% through heating it from 50 to 120F, this is not enough safety. After heating water, some of the bubbles leave the water. This can be evidenced by the spurting and release of air upon opening some taps. So the whole ‘pressurized vessel’ of the water system bottled up by a backflow preventer can then cause an excessive pressure as the heated water expands into the cold water side as well.
So every time you install a backflow preventer, double check, or pressure reducing valve separating the domestic system from the main you are creating a possible problem that the T&P valve has to handle alone, unless you add an expansion valve.
Adding another check before the water heater after already causing an isolation with a backflow preventer simply isolates the problem expansion to the hot water side, which should have an expansion space to prevent lifting the T&P as the water is heated.
This is, after all, the purpose of an expansion tank in a modern hot water system, which is always a sealed system isolated from the cold water system by a pressure reducing valve, check valve, or backflow preventer, unless it is totally isolated by hose fill.