No, it is exactly as complicated. As demonstrated by its utilization of exactly the same mathematics.
Not all formalizations that give the same observed predictions have the same Kolmogorov complexity, and this is true even for much less rigorous notions of complexity. For example, consider a computer program that when given a positive integer n, outputs the nth prime number. One simple thing it could do is simply use trial division. But another could use some more complicated process, like say brute force searching for a generator of (Z/pZ)*.
In this case, the math being used is pretty similar, so the complexity shouldn't be that different. But that's a more subtle and weaker claim.
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The interpretation in this context can imply unobserved output. See the discussion with dlthomas below. Part of the issue is that the interpretation isn't separate from the math.
"Entities must not be replicated beyond necessity". Both interpretations violate this rule. The only question is which violates it more. And the answer to that seems to one purely of opinion.
So throwing out the extra stuff -- they're using exactly the same math.