So the only thing they did was make a bad model?
The Amazon Molly parthenogen species complex is know for many years as just that; the females need to be stimulated in some sense by the presence of male sperm but then go on with the standard split-my-own-cells-and-stick-them-back-together way of sexless reproduction. So that's not news.
Many models try to explain why this is bad, and really so bad that it's even worse than sex(*). It goes all the way back to famous brit RA Fisher, pointing out that if a mother makes 2 daughters per generation (as will those) then your population doubles every generation; if a mother has to make 1 son and 1 daughter per generation (to mate with another mother's offspring) at the same cost, then the population stays at the same level. (If both make 4 children, it's "doubles" versus "quadruples", etc.) This is the famous "2-fold cost of sex". So any heritable trait that lets you avoid this cost will be very advantageous.
So what they in the BBC article claim to have done, is make a model along these lines, run the numbers and find out the outcome didn't fit. Thus only pointing out some assumption somewhere is wrong? I don't get it, are peer review standards slipping?
The most typical arguments contra parthenogenesis are M"uller's Ratchet and similar, that the recombination in sex allows you to combine good, or less-damaged, genes with other good ones and maintain your population's health; without recombination you will eventually have bad mutations in each gene and no way to improve this. [One way to repair this is recombination-with-yourself, so that the daughter is not an identical copy of you, but in each locus has either both alleles that the mother had or two copies of one of the two --- drawback is that you lose a lot of variation until everybody has 2 copies of the same allele in each locus anyway; but after that it's a good way to repair your genome.]
But these not-working models or not-fitting numbers are old news; a working one would be good news. Hm.
*No it didn't surprise anyone that it was an (very very late-victorian) englishman that tried to convince the world what a pointless and costly distraction sex is.