The person who wrote the quote has an axe to grind. First off, a priori logic is not how you figure out Biology or Evolution. Experiments establish that knowledge.[Logic 101]
However. This kind of logic is extensively used in Apologetics. This discipline is essentially devoted to proving that your religion is correct and others are not.
https://en.wikipedia.org/wiki/Apologetics
Christian apologetics (the proposed argument above) is more, um, adamant about defending the faith. When used by Biblical fundamentalists you get arguments like the one above. Conservative Christians view Evolution as an affront to their views.
https://en.wikipedia.org/wiki/Christian_apologetics
[/Logic 101]
Importantly. Aside from all that, the quote conveniently ignores mutation, which occurs spontaneously. It is true that if a population of organisms gets cut off from the main one, it likely has a different set of gene frequencies and is missing some genes (alleles) as well. This is called the founder effect. The rate of mutation for the isolated population continues unabated. So new DNA becomes available.
https://en.wikipedia.org/wiki/Founder_effect
Note: when you read this remember that scientists use the word 'theory' to mean something well-tested and documented. It is nothing like when your friend comes up to you in casual conversation and says, 'I have a theory about why Jenny likes Billy' The two meanings are light years apart.
So, a counterpoint based on experimental evidence starts with:
https://en.wikipedia.org/wiki/The_Theory_of_Island_Biogeography
- remember the the admonishment about 'theory'
And Darwin's finches as well, but you have enough to read already.
Living organisms acquire mutations "spontaneously". An example of this is environmentally induced cancers.
https://www.niehs.nih.gov/health/materials/cancer_and_the_environment_508.pdf
Somatic and sex cells in organisms may develop changes in DNA (mutations, deletions, additions) from exposure to: heavy metals, many kinds of organic molecules, background radiation. If the DNA change affects the control of cell division or "turns on" a gene that should be off, it often affects cell division and cell differentiation in the tissue where the DNA change occurred. This anomalous growth is a tumor.
@FactChecker - the quote does have a point and it is not about Evolution. It is about the correctness of certain theology.