The CEOs don't need to be paid by other companies. All a competing company needs to do, is to convince some company's board members to hire a CEO with a track record that they know will tank the company... maybe through indirect lobbying, maybe by hinting they want to hire them because it's "such a valuable CEO"... and bam!

CEO ruins company, then bails on a golden parachute, and you only had to spend whatever it took to mislead the competing board.

(I've seen it done to tiny companies with as few as 20 workers, it's surprisingly easy to convince a board to hire someone who will destroy everything)