Following the 1989 regular season, Everett was reportedly "shellshocked" from the multiple times he was sacked and hit in the NFC Championship game against the San Francisco 49ers (the 49ers won, 30-3). At one point in the game, Everett was so rattled that he collapsed to the ground in the pocket merely in anticipation of yet another sack, even though the 49ers' defensive players actually had not yet reached him; a play now known as Everett's "phantom sack". From then on he was perceived to shy away from hits, and later acknowledged that his confidence was never fully restored.
This reputation led to Everett's infamous 1994 confrontation with then Talk2 host Jim Rome. Rome had made a habit of repeatedly mocking Everett's reputation for being averse to taking hits by referring to Everett as "Chris" Everett (a reference to female tennis star Chris Evert). Everett appeared as a guest on the show and Rome wasted no time, applying the insult twice within the first 10 seconds of introducing Everett. Everett warned Rome not to do it again, implying that physical consequences would ensue otherwise. Everett, visibly angry by this point, then went on to challenge Rome, predicting that now that the warning had been issued, Rome wouldn't dare to repeat the insult again. Rome promptly applied the insult a third time and Everett responded by physically charging Rome, overturning a table and knocking down Rome live on air before leaving the set. This incident was later parodied on an episode of Cheap Seats with Randy and Jason Sklar portraying the two.