These claims can actually be roughly divided into degrees by severity. The mildest possible degree is when someone does agree that there are seeming contradictions between what the religion's holy book says and what we can observe in nature, but it's not a question of the book being erroneous, it's simply a question of interpretation (eg. it's just metaphorical text, or we are misunderstanding what the text actually means.) A higher degree is when someone outright claims that there is no contradiction whatsoever between science and the religion's holy book. (Usually a rather wild amount of handwaving goes to try to explain the contradictions away. Or alternatively to redefine what's meant by "science.")
However, the highest degree of taking credit, the most obnoxious one, is when someone claims that not only are there no contradictions, but in fact their holy book actually spawned scientific research and knowledge, and that said book contains advanced scientific facts that were only corroborated centuries later.
For some reason many muslims are fond of making this curious claim. They actually outright say that modern science originated from Islam's holy book. Some go even so far as to completely ignore history and claim that before said book humanity lived mostly in chaos and self-indulgence, and had little to no curiosity about how the universe works, and that it wasn't until the koran was written that actual scientific progress started.
I just finished watching a "documentary" that made incredibly obnoxious claims like that. It claims that before the koran there was little to no scientific curiosity, and that the koran spawned most branches of science. It says things like:
When we look at the verses, we find indications of all the main branches of science in the Koran. For example, in the Koran God encourages the science of astronomy like this: "He Who created the seven heavens in layers. You will not find any flaw in the creation of the All-Merciful. Look again - do you see any gaps?"This "documentary" is full of laughable claims like this. (Come on, "the seven heavens in layers"? What's that supposed to mean?)
In general, in these types of claims there's willful ignorance of history. Scientific curiosity and discoveries have existed for over a thousand years before the koran. Moreover, science has always thrived the most when it has been independent of any religion.
Most importantly, though, Islam didn't spawn science, but on the contrary, it killed it. Two millenia ago Greece was basically the world capital of science, but the Roman politics and wars, and especially the Roman church, killed it. After that science moved mostly to Arabic countries. In those countries science thrived in spite of religion, not because of it. For a time scientific progress and Islam co-existed, but at some point islamic imams decided that mathematics and science are evil and banished the practice, which basically killed scientific research from Arabic countries.
For centuries the world lived in the dark ages, scientifically speaking. In Europe the Roman church, later the Catholic church, stifled science almost completely. In Arabic countries Islam did the same. It was not until the so-called Age of Enlightenment, when a new counter-culture raised with the ideology that science should be separate and independent of religion, that science thrived once again.
No religion has ever promoted or encouraged science, but the exact opposite. Science has always advanced when religion has not been killing it, when scientists have had the opportunity to make research and discoveries without religion meddling in their work. I can only imagine how advanced we would today be if neither Christianity nor Islam, or any other like religion, had ever existed.
No scientific discovery of any importance has ever been produced by either Christianity or Islam. The major difference between those two religions is, however, that Christianity has (mostly) stopped meddling with science, education and progress, thus allowing for giant leaps in scientific progress, while Islam still wants to live in the 7th century.
(Just as a testament of this, count how many Nobel prizes have been awarded to arabic people, and how many have been awarded to non-arabs. And we are not talking about the useless peace prize here. This is not a question of racism or anything like that. This is because high education and scientific research is not promoted nor encouraged in the vast majority of arab countries, purely for religious reasons; thus is it any wonder that no important scientific discoveries are ever made there?)