Earlier quoted context omitted.
Any evidence to support this? I've heard otherwise.
Yes it follows from first principles, a well-insulated house has a structure that is being heated and retains heat (like a pizza stone) as well as the air itself. Heating air inside a cold structure is quite different from heating air inside a warm structure. So your evening heating will have to work harder to warm the structure back up that was allowed to cool in the day. The air in the evening will cool faster and…
As far as thermodynamics, you're always exchanging heat with the environment. Only the coefficients change with different insulation levels. And these losses correlate with the gradient between the inside and outside. When the gradient is zero, equilibrium means zero net heat transfer. When the house is allowed to drift towards the outside temperature, the total losses will be lower than if comfort were maintained through those same hours. The integral (sum) of these loss rates over time is your total energy loss and a good proxy for the total energy needed from the heating system to condition the space.
The whole tradeoff is about comfort and convenience to have the space conditioned when you want it and to have an appropriately sized system for the needed load. Whether oversized or undersized, equipment may not operate efficiently if asked to operate outside its designed load level and duty cycle. It can also become unreliable with the wrong duty cycle, i.e. a small unit asked to run too long and too frequently or a large unit asked to run too infrequently and for too short a duration each time.
That the equipment has to operate at a higher load during recovery does not imply that it actually uses more total energy in the daily cycle. That would only be true if the equipment is inefficient at the recovery load. An example where this is true would be a heatpump system with an auxiliary resistive heating element that engages in recovery. But, a gas furnace or a sufficiently large heatpump is likely more efficient in recovery since it is also working with a larger gradient until recovery is complete.
It is common for basic clock-based, programmable or smart thermostats to allow for daily drift to save energy. They use a more comfortable set point during morning and evening hours when occupants are most sensitive and then allow some drift towards ambient during midday and nighttime hours when occupants are less likely to notice. This is precisely to leverage this tradeoff to have less total energy losses per day. They don't completely turn off but vary the set point so that the building is kept within a range where the comfortable and efficient recovery is possible. Depending on the day, this might be equivalent to turning off or it might just reduce the duty cycle slightly.