I agree with some of that paper’s conclusions. But there is nothing there that is surprising. When a hypothesis is tested, especially in the case of complex ones, the hypothesis itself is rarely directly testable. Instead a testable prediction is deduced from it. In essence what one does it this: If H is true, then so is I, where H is the complex hypothesis and I is the testable (in theory) prediction. This gives us the first step in the following test in syllogism form.
Premise 1: IF H is true, then so is I.
But as is almost always the case in complex hypotheses, the deduction of I from H is never an easy step. The deduction is not clean and usually introduces a number of hidden assumptions or auxiliary hypotheses, A1 and A2 for example, so the premise actually looks more like this.
Premise 1: If H, A1, and A2 are true, so is I.
So, then when I is tested, so must A1 and A2 be tested. But often these auxiliary hypotheses are not immediately obvious to the scientist, so they are not tested initially. It is only after the hypothesis is falsified (i.e., falsely falsified, one might say) and the dogged scientist refuses to give up are these auxiliary hypotheses discovered and tested separately. So, far from being a problem that the paper you linked to suggests, the recognition of these auxiliary hypotheses is a good thing because it forces the scientific community to come closer to the truth in their complex hypothesis testing.
That model of speciation you describe is in fact the allopatric model that is believed to be responsible for most speciation. However, the formation of a million or so species (a conservative, approximate number of extant species) in such a short span of time still boggles the mind.
By the way, evolution does not necessarily require additional mutations beyond the ones already involved in existing genes that are recombined. The requirement for evolution may be met by recombination of existing genes into new arrangements that may suffice to introduce genetic variability that natural selection can act upon. So, what is required in evolution is genetic variation, which can be produced by new mutations or by simply rearrangements of older genetic material in new ways. An extreme example of this occurs in speciation by polyploidy, in which there is absolutely no new mutation at all. What happens in this case is an increase in the number of chromosomal sets beyond the usual 2. What we see in speciation by polyploidy is an instantaneous formation of a new species as the offspring generation receives abnormally 3, 4, or even more sets of chromosomes compared to the 2 in the parents. The offspring cannot interbreed with the parents because of lack of chromosomal pairing at meiosis, the process that produces gametes, but they can among themselves.
I have heard the term used as a pejorative paired up, usually, with ‘creationism’, by fools that don’t know any better.