No Recording Rule at Work: Pro and Con

Is it lawful for an employer to prohibit employees from recording (in any fashion) conversations, phone calls, images or company meetings with any recording device unless prior approval is received? That is Whole Foods' policy. Its purpose is to foster open communication, even disagreement. Some workers, who are organizing a union, have won a ruling from the NLRB that strikes down the employer rule as anti-union. I disagree with the ruling, and believe a court of appeals will overturn the ruling. The company policy is long-standing and was not implemented to thwart the union; and more important, its purpose was to increase employee voice, not to suppress or manage it.