The source appears to be William Shatner's documentary Chaos on the Bridge and detailed here
Stewart was famously The Serious One among the cast in the show's early days, and wasn't pleased when the other actors took time to goof off on set, but his stern focus apparently hit a new level early in Season 2 when he refused to read a particular line in a script. In Shatner's film, showrunner Maurice Hurley claims that, when he got the call from the set that Stewart was refusing to go on, he responded with "Fire them all," and declared he would blow up the Enterprise and rebuild the second season with an entirely new crew.
The issue with Stewart eventually went up the ladder to John Pike, head of Paramount Television, who decided he'd settle the matter through a lunch meeting with Stewart. Pike, who knew how to play the Hollywood game, scheduled the lunch when he knew Stewart wouldn't have time to change out of his costume, and deliberately arrived 15 minutes late, so Stewart would have to sit alone in the executive dining room on the Paramount lot dressed as Captain Picard. When Pike finally arrived, he wasted no time.
“I say, ‘Patrick, let’s just cut through it. I do know that you’re creatively not being taxed. You’re going to have to bear with us for a couple more weeks, but we have already put the script in the works and we will write your character out,'" Pike said.
Stewart asked Pike, "What are you talking about?" and Pike responded, "The one thing I don't want is my lead actor unhappy." Instead of calling Pike's bluff, Stewart apparently relented, and according to Pike, he "never had another discussion" with Stewart about the issue.