No. It is not true. The regulator adjusts the mechanism so that when the natural disc is engaged, it raises the pitch exactly a half step, and when the sharp disc is engaged, will raise the pitch another half step. The mechanism will do this regardless of what the instrument is tuned to.
In theory-and this is stretching reality to the absurd-a higher tuning would pull the soundboard up slightly and the neck down slightly, thereby shortening the strings and throwing the regulation off. By this idiotic argument, lowering the tuning would allow the soundboard to flatten slightly, lengthening the strings and throwing the regulation off. But a difference of 2 beats per second is, in reality, not going to change anything about the string length.
.
