In fact, they used the same data as other scientists who used parsimony, and got very different results.
In other words, the conclusions do not follow from the data, but rather from the assumptions made in interpreting the data. Other scientists use an assumption they call "parsinomy"; the current authors use one they call "maximum likelihood".
I went and read the paper - it's online, just follow the links - and here is my short analysis.
We have two critters - A and B - presumed descended from a common ancestor, X. Where the genomes of A and B are identical, we assume those bits inherited from X. But what of the differences? Let's say that A has a feature F (specifically in the paper, an intron - look it up to find out why this is important), and B does not. There are two possibilities.
(1) X had the feature F, A inherited it, but B lost it.
(2) X did not have F, B duly did not inherit it, and A gained it.
Clearly, assumption (1) leads to the conclusion that features are gradually lost, which means genomes are becoming simpler over time. And assumptionm (2) leads to the exact opposite conclusion.
Well, which is right?
I don't know, and neither it seems do the experts, but what I do know is probability theory, and the key section of the paper, which is all about probability theory, is flat wrong. Here is my analysis.
Once two lines of descent have split - as X split into A and B - their subsequent histories are independent. This leads the authors to suppose that the probability that A will gain an intron (F) is independent of the probability B will gain one, and vice versa. That is dubious, but since they don't use this assumption it doesn't matter. (To see why it's dubious, would you agree that chickens and ducks have completely independent susceptibilities to bird flu? I hope not)
But the assumption they do make is even more dubious, namely that the probabilities A or B will lose introns are independent. This is the basis of their initial probability equations, which are based on the assumption of independent probabilities of intron retension, and hence of their entire conclusion.
But that assumption cannot be true. If we investigate A, say, and find F, we assume A has "retained" F. But when we now investigate B, and find it lacks F, our interpretation of the data must take into account what we know about A. In other words, what would be the probability B has lost F, given that A has retained it. That is proper Bayesian reasoning, and it dramatically affects our interpretation of the evidence. In particular, if an intron has been retained by A, this greatly increases the posterior probability it would also have been retained by B, and hence casts serious doubt on the prior assumption of retention.
To cut to the chase: the author's assumption of independent probabilities gives a much greater likelihood for the assumption of retention rather than acquisition, and hence a much larger estimate for the complexity of the early genome.
The author's conclusion is a consequence of their assumptions, and in my opinion the dramatic nature of the conclusion is entirely an artifact of error in those assumptions.
First it should be noted that the authors that you are refering to are secular Harvard Biologists and not the Creationist writers who summarized and excerpted the data for Creation Evolution Headlines.
Also, it's not as simple as A & B, they were comparing 7 fully mapped Genomes.
I followed the links but didn't get to the article. It wanted me to subscribe for a fee.
But I didn't really follow your logic. Given that the ancestor X had the intron, I don't see why B's retention would depend on A's retention at all. It seems to me that they would indeed be independent.
I assume they are determining what X had by looking at the introns across the 7 fully maped genomes. It would be logical to assume that if an intron is found in multiple organisms that it was inherited. Otherwise the means of acquiring the intron must be determined. Simple mutation would be ruled out since introns are strings of code involving up to 500 pairs.