Is this true in a turbocharged aircraft or for that matter any aircraft that is flat rated to a given altitude?
Yes, it's true, but the decrease in the effective minimum single engine control speed (which isn't the same as Vmc...Vmc is a certification number) isn't as large with a turbocharged, supercharged, turbosupercharged, or turbocompound engine.
The engine can only output so much, and regardless of whether the engine output remains the same (a turbo normalized engine, for example), the propeller efficiency decreases with altitude due to a decrease in air density. Less thrust, less assymetrical thrust, lower real minimum single engine speed required to achieve the same result.
Remember that Vmc is a function of assymetrical thrust, which is an indirect effect of engine performance. The engine still has to turn the propeller, which must act on the atmosphere to produce that thrust. Decrease the thrust (a function strictly of blade angle, air density, and RPM), and you decrease any potential for thrust assymetry, and therefore the value of "Vmc" decreases. Just the same as if you reduced power on the good engine.
Vmc is a solitary number, and in most cases, it doesn't go up or down appreciably. Some AFM's publish variable numbers, but it's generally given as just a red radial reference line on the airspeed indicator. That aircraft control is actually lost at this point is merely a coincidence. Numerous factors can decrease the actual speed where directional control isn't possible, and various factors can increase the number...all while Vmc remains the same. Actual performance isn't the same as Vmc. Vmc is a paper number, not what's going on in the airplane.
We generically refer to what's really going on in the airplane as Vmc to make it simple, but this also tends to confuse the issue sometimes when talking about the science behind it.
I believe this generally held belief is due to DA decreasing with altitude and consequently less air molecules available for combustion, and therefore less power produced, and therefore less torque, and therefore a lower Vmc speed in non-turbocharged aircraft.
Density altitude
increases with altitude, and with an increase in air temperature. It does not decrease with an increase in altitude except in the case of a strong temperature inversion, and then only for brief periods.
Regarding the wings; Because DA reduces with altitude there are less molecules of air hitting the front of the Pitot tube, so therefore we are trained to understand and use indicated air speed, IAS. Or to paraphrase, IAS is always used by pilots because IAS automatically compensates for DA. Therefore as pilots we understand that IAS is not TAS but to use IAS for all maneuvering decisions and understanding that true airspeed is higher due to effects caused by DA.
The wing is irrelevant to the question, because Vmc is a function of assymetrical thrust and control availability (chiefly rudder). Center of gravity makes a difference, but the reason the minimum control speed decreases with altitude (again, DA, or density altitude does not decrease with an increase in altitude) is a decrease in assymetrical thrust. This is more pronounced in a normally aspirated engine, but still exists in a turbocharged engine for the reasons previously given.
Does the IAS Vmc speed reduce in an aircraft that has flat rated engines as DA increases?
Again, Vmc may never change, because it's a single number, and is painted on your airspeed indicator. The actual number at which directional control can no longer be maintained (the effective Vmc, if you will), does decrease...even if the engine is normalized to maintain the same power output as altitude decreases. The engine still has to drive the propeller. The engine doesn't produce any thrust of it's own accord (save for a few circumstances where exhuast gas does produce a very slight thrust quotient). It's the propeller doin the work moving the air, and it's propeller efficiency that decreases with altitude.
Additionally, while one flies the same airspeeds with an increase in density altitude, as one climbs the air density and aircraft reaction does not remain in proportion. This isn't greatly noticable at lower altitudes, but it is the higher you climb.