It is not the exact phrase, but I have heard variations of this claim. I am wondering whether such claim is supported by a study or experiment. I am also curious if there is a way to sort of vaguely quantify memory. In other words, is there a way to know how much memory/resources a type of task occupies? For example, is it possible to know experimentally whether the muscle memory required to play a piano needs more memory/resources than the memory needed to read a piano sheet?
First, consider that those questions can potentially be answered only in animals, like mice. There is no way to test such things in humans, because methods like fMRI give resolution of $\approx$1,000,000 neurons. In order to test your hypothesis, you need resolution below the neuronal level, because what your need to see is how the connections (synapses) between neurons are established. Theoretically, you can train mice to run a maze. Then, with a microscope, one can count how many synapses were created. I think, to date, you cannot do this without killing the mice. If so, then you will take other mice and teach them to play piano :) So, the difference between change of connections might be your estimate. But you cannot know whether two tasks are equivalent, so you may end up comparing apples and tomatoes. Overall, the term "memory" is not something that is precisely defined on a biological level, like RAM or hard-drive capacity on a PC. There are prominent hypotheses about how memories are created (connections between neurons), but those are still hypotheses.
You might be interested to read this book; hopefully it is not too complicated without much background: Connectome: How the Brain's Wiring Makes Us Who We Are (Seung, 2012)
Seung, S. (2012). Connectome: How the brain's wiring makes us who we are. Houghton Mifflin Harcourt Trade.