It's unnecessary to read the definitions that you link to when the article that the OP is speaking about explains what it is referring to as intuition. It is different from the regularly understood meaning of the word. The article is not talking about intuition in the dictionary sense, but rather exactly the way I termed it, the processing of information that is available to the person without conscious reasoning.
Read the article. scoff at it if you wish. But at least talk about the terms in context with the basis of the conversation.
According to your quote,
"“Studies show that the frontal lobe in the cerebral cortex is more active in women,” says Amen. “In part, because the white matter here has more connections, and therefore, women are able to pick up on more emotional cues like facial expressions.”"
serves to support the notion that anything a human perceives is only through the 5 senses we have - touch, smell, sight, sound, and taste.
That the frontal cortex may be better developed in women allowing them to detect emotional cues better, it is still via the senses.
However, many who believe in "intuition" seem to not know how they come to their knowledge. They resist that it is their senses at work, or don't make the connection between their senses and knowledge. It is as though they think that "intuition" is a form of supernatural power. Therefore they deny any form of rationality in their knowledge.
The fact of the matter is, is that highly developed consciousness is able to discern what is detected by the senses and how facts are connected to those senses. Undeveloped consciousness cannot discern how the knowledge was attained and facts assimilated. I would conclude that the "highly developed frontal cortex", or "intuition", is simply a nice way to avoid the pertinent issue - and that is, an undeveloped consciousness of perception. The motive for giving the "highly developed frontal cortex" reason is probably nothing more than political correctness for fear of offending women folk.
Now if one were to claim that "intuition" or "gut feeling" is some form of supernatural power, then it is outside of rational discourse and indeed the scientific framework. Frankly such people are either completely irrational, stupid, or are geniuses with special gifts. I for one believe in supernatural powers, but "intuition" is not one of them; it is still in the realm of the senses.