An example I am aware of is the Torah Codes, in which the birth and death dates of important Rabbis are supposedly encoded close to their names in the Bible. Some very intelligent researchers found extraordinarily strong evidence using recognised statistical techniques, and their results were published in a secular peer-reviewed journal. It had many people convinced for a time, until other researchers demonstrated methodological problems that were the probable source of the amazing evidence. It is likely that the researchers "tuned" their experiment, settling on a sample which confirmed their hypothesis, and then presenting their tuned sample as an independently compiled sample.
When you disregard confounding evidence, as is common with religious belief, any statistics that you use as justification for your beliefs is automatically useless. Based on this, I think it is extremely hard to take seriously research done by people with religiously predetermined opinions.
Meaning of "Intellectual Honesty"
The standard of intellectual honesty is more rigorous than just having knowledge.
For instance, true belief does not consititute knowledge. For knowledge it is necessary that a believer have justification to support their belief. But the believer must only be aware of the justification for their belief for it to be knowledge. The belief need not be caused by the justification.
In contrast, I don't think that simply having justification constitutes intellectual honesty. It is not just necessary that the believer is aware of the justification, I think they must believe an assertion because of the justification, or at least be open to disbelieving it should the evidence point in the opposite direction.
While an (hypothetical) entirely irrational person may have true beliefs and untrue beliefs, none of their beliefs constitute knowledge because the truth of their beliefs is accidental. They do not know (or understand) the difference between their true and untrue beliefs.
Likewise, a person with an overriding faith may have justified beliefs and unjustified beliefs. Although they know and understand justification, this time they simply do not care about it. Whether their beliefs have justification or not is accidental, and so the truth of their beliefs is still accidental.
Such a person may be very intelligent, and may in other ways be honest, but as the truth of their beliefs is still fundamentally accidental, it can be difficult to trust them. Even without lies, if they do not believe because of justifications, and would not be able to be swayed by justifications, they are still intellectually dishonest.