Sometimes man generously spoke of something. Don't take it seriously. Do u think Jiriya could beat BEE, whereas Kisame almost got him if A didn't interfere. Please consider the situation when Kisame n Itachi meat Jiriya.. It was very early in the manga. Definitely Kishi couldn't risk his manga's future by showing off too many powers, which was also seen in Hiruzen VS oro's fight. It was a very lame fight considering the skills of both Hiruzen n Oro. If u compared that fight with present day fight, it was nothing. So, don't take Kisame or Itachi's word as a source to measure Jirya's ability.
If Itachi was determined, he could take captive Naruto by then. But Itachi's true intention was to make a appearance in Konoha for Sasuke's safety (which was told by Tobi). Whether u believe it or not, Itachi was never intended to engage in serious battle with Konoha's people. If so, he could have killed Kakashi.
No doubt Jirya is a versatile n eminent ninja. But, I assume still he is below Itachi.
Konan was once Jirya's apprentice and Jirya's knew about Konan's ability. So, he could find weakness in Konan's ninjutse very quickly.
As far Nagato's word, Jirya could beat him if he knew his secret: this is also a word to honor his former sensei. But in reality, Jirya could never beat Pain, which was also supported by Fukusaku.