There is no direct historical document supporting the claim that the chili pepper entered Korea during the Japanese invasions of 1592-1598. The only basis in the historical record is "Jibong Yuseol," a book published in 1614 by Yi Su-gwang. It contains an account of the arrival of "nammancho," a pepper that could kill a person if mixed into liquor and drunk. To argue that the Korean chili pepper arrived during the invasions, nammancho would have to be the Korean chili pepper. But there is no record of anyone dying after mixing Korean chili pepper into liquor, and in practice doing so would not cost a person's life. From the standpoint of evolutionary science, nammancho could not have become the Korean chili pepper within 100 to 200 years. Genetic analysis indicates that at least several million years of evolutionary distance separate that pungent pepper from the Korean variety.
In China, chili peppers went by several names. Peppers grown in the Sichuan region were called "chuncho," those produced in the western regions "hocho," those from Nanyue "mancho," those brought in from Indonesia "nammancho," and the variety from India "beoncho." Among these, nammancho could indeed prove fatal if mixed into liquor and consumed. Kim Jong-jik's "Jeompiljaejip" records that liquor mixed with chili pepper was drunk at ancestral rites, and there is also a record that Kim Jong-seo and his men drank liquor mixed with chili pepper during the bitter winters while opening up the Six Garrisons. Another record describes sweet rice drink mixed with chili powder being taken as a cold remedy. Paradoxically, the account in "Jibong Yuseol" is not a record of the Korean chili pepper arriving during the Japanese invasions but rather evidence that the Korean chili pepper already existed before then.
The account in "Jibong Yuseol" is more accurately read as a record of the arrival of nammancho, one type of chili pepper. In that respect, it is difficult to call nammancho the Korean chili pepper. Had a pepper that pungent been the one available, kimchi and gochujang could never have come into being.