Earlier quoted context omitted.
It's not a burden of proof situation because your boss is paying the bill. But, if it was about who claimed what, the employees are the ones making the claim that "remote work is just as productive".
If it's about the boss's power, they can always just fire people who won't come into the office. If the boss doesn't want to do that, they've got to do the convincing. You either convince people or order them around and live with the morale consequences.
If you need convincing to return the the office you were hired to work in then you probably aren't the type of employee a boss would want to retain.