There's more than one way to verify a conclusion.
For example, if I say that RSA-130 = 39685999459597454290161126162883786067576449112810064832555157243 × 45534498646735972188403686897274408864356301263205069600999044599 then you can easily verify it by multiplication - you don't need access to the factorization software I used to determine that result.
If I say that the energy difference between two chemical structure according to the Merck Molecular Force Field (MMFF) is X, then you can use any software which implements the MMFF to verify my statement using the raw data - you don't need the source code that I used.
In fact, it would be better to use an independent implementation to verify my result than it would be to re-run the same code. And there are many programs which implement the MMFF.
If you are used to RDKit, then it will likely be faster to use RDKit to reproduce and verify my numbers than trying to figure out the strange VM I provided, which is based around some home-brew code of mine implemented in MORTRAN.
I didn't write about independent computation, but about independent verification. In your case you need access to a software for multiplying numbers for an independent check. OK, this is rather trivial code to write. But if it weren't that trivial the author would have to provide it.
But I question the meaning of your phrase "independent verification".
If the author has to provide the program used for verification, how is that "independent"? At the very least, isn't there a range of dependencies, from "running the same code in an identical environment produced the same answer" to "running a different code in a different environment produced the same answer"?
Which verification do you trust more? What level of independence do you need before you can trust the results?
Let me give you a few other examples. "We docked 500,000 small molecule structures from CHEMBL against the target using 6,000 GPU days. We took the 1,000 best fits and measured binding affinity. The top 10 structures are shown in table 1. The third is our lead candidate, which reduces the chance of infection in rats from 80% to 10%."
Do you need to be able to validate the docking results in order to accept this paper as science?
"We used ProteinFitter 4.5 in simulated annealing mode to generate the best protein fold to the given constraints. The resulting structure has a R-factor of 2.3Å against the Hodgkin electron density, which is better than any other published model."
Do you need access to ProteinFitter 4.5 to verify this paper? Since all crystallography tools will generate an R-factor for you, why is it critical for the model provider to also supply an environment which contains a tool which does that?
Both are examples where it doesn't matter what's in the magic box, or if the magic box is buggy. It could as well be "I had a dream about a snake tying itself into a knot and eating its own tail. I woke up and realized the structure might be a trefoil. It fits all of the known data and makes intuitive sense and hasn't been considered before, so I'm publishing in the hopes that others can explore it more rigorously."
Is that science? I say "yes".
Now, replace "dream" with "computer program" - is it still science? I still say "yes".