Debunking another myth about value types

Here’s another myth about value types that I sometimes hear:

“Obviously, using the new operator on a reference type allocates memory on the heap. But a value type is called a value type because it stores its own value, not a reference to its value. Therefore, using the new operator on a value type allocates no additional memory. Rather, the memory already allocated for the value is used.”

That seems plausible, right? Suppose you have an assignment to, say, a field s of type S:
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