There was some truth to that in the past, not applicable to modern vehicles. In the past, one of the heater hoses had a valve in it that controlled the amount of hot water that entered the heater core. When the engine was cold and that valve was closed, and naturally the thermostat was closed as well, when the engine was started, there was virtually no flow of coolant in the engine.
It took a while for enough heat to reach the thermostat to get it to open. That could cause the coolant in engine to heat up at different rates depending on how close it was to the heat sources. You could have areas that were overheated until the thermostat opened up. Sliding the heater control all the way over to hot would allow some coolant to circulate allowing the coolant and the engine to heat up more evenly. Fan position had little effect.
In old cast iron engines, this wasn’t really a problem. Cast Iron is more resistant to warping and blowing gaskets. Todays engines do not have a heat control valve in the heater hoses. Heat is controlled by blend doors. The coolant flows through the heater core all the time. Anything you do is irrelevant.
There was a long discussion similar to this years ago but it had to do with the fastest way to get heat into the passenger cabin. I believe the consensus was that turning the heater fan on right away was the quickest way, but it was also the most uncomfortable because the initial air would be so cold. I think we agreed the most comfortable way was to wait and turn the fan on after the needle on the temp gauge got off the cold so that the air would have some heat in it, but you didn’t have to wait until the engine was all the way up to operating temperature.