pull the wool over someone's eyes

今日取り上げる慣用句もASJ３月例会の会報にあった表現です。
I met very nationalistic and very leberal thinkers as well. One shoudd check facts and back them up: check for wool being pulled over one's eyes.
"wool being pulled over one's eyes" の意味が分かりません。一瞬、目からうろこを連想したのですが、意味が通りません。辞書を引くと全くのその反対の意味でした。
"pull the wool over someone's eyes" で次の説明があります。
・McGraw-Hill Dictionary of American Idioms and Phrasal Verbs: Fig. to deceive someone. You can't pull the wool over my eyes. I know what's going on. Don't try to pull the wool over her eyes. She's too smart.
・Cambridge Dictionary of American Idioms: to deceive someone These people who claim to have paranormal or supernatural powers are just pulling the wool over people's eyes.
・The American HeritageR Idioms Dictionary: Deceive or hoodwink someone, as in His partner had pulled the wool over his eyes for years by keeping the best accounts for himself. This term alludes to the former custom of wearing a wig, which when slipping down can blind someone temporarily.