It’s widely acknowledged by automotive engineers that most engine wear occurs within this first ten minutes of driving before the engine has reached its highest, normal operating temperature.
When you first start the vehicle, do not race the engine. Accelerate gradually until the engine (and the rest of the drivetrain) has completely warmed up; it takes about 10-15 minutes, depending on the outside temperature. Most engine wear occurs at cold-start and during the first few minutes of operation. Revving a cold engine will greatly accelerate this wear and tear.
Basically, yes. It is true, and basically it's because the oil has settled and is no longer properly lubricating all the parts, creating a greater amount of friction and consequently, wear.
For a more official source, check out https://www.motorists.org/blog/things-we-do-to-cars/.
And Jim Kerr from the Automobile Journalists Association of Canada writes,
Most engine wear occurs in the first couple minutes after a cold start. Rich fuel mixtures wash lubrication from the cylinder walls.
Thick oil doesn’t spray onto moving parts as easily, so using a winter grade oil will help reduce engine wear.
When the engine is first started, the oil pump forces oil into the oil passages and through the oil filter.
The pleated filter element may restrict thick oil too much, so a bypass valve is designed into either the oil filter or the engine itself so the thick oil can bypass the filter.
Oil may bypass the filter for only a few seconds or for nearly a minute if temperatures are cold and the oil viscosity is high.
During this time, unfiltered oil flows to the engine, which is better than no oil, but it still allows dirt particles to flow to moving parts.
Changing to a winter grade oil with lower viscosity helps keep bypass times short and provides faster lubrication to moving parts.
And for a published resource, check out Vehicular Engine Design - Powertrain by Kevin L. Hoag, ISBN 1613-6349, p. 136.
Citations from the Society of Automobile Engineers:
In this study, cold start wear tests were conducted in a cold room with temperature control ranging from +25°C to −40°C. Wear data of methanol engines, under starting conditions typical of the Canadian environment, are compared with data of a gasoline counterpart. The analysis of these data so obtained suggests that a temperature dependent theory is valid to explain the cold start wear results. Further, the cold start wear can be a significant portion of the total wear and is attributed to the direct attack of methanol on the cylinder walls in the first few seconds of engine operation.
Studies in laboratory engines equipped with radioactive piston rings show that wear is highest during a cold startup. Corrosion by condensed combustion products is responsible.Engine operating variables and additives in fuels and motor oils influence corrosion and, therefore, startup wear. Long shutdown periods, low engine temperature, and high intake-air humidity increase wear. In fuels, antirusts offer some control; for example, an amine dialkyl phosphate eliminates 40% of the wear.
NB: Special thanks to @DucatiKiller for his assistance