Tbf, it's the 4 day workweek advocates explicitly making the claim that everyone's output curves become negative on the fifth day such that 32hr output ~= 40 hrs output.
Legal restrictions on working hours weren't put in place with the assumption that firms no longer being able to demand 80 hours from their employees couldn't possibly lose any output as a result. That was done because governments decided 80 hour weeks were unreasonable.
The argument can be more complicated than just "the company will be more productive." Examples are "society will be overall more productive" (because the free time will be used productively), or "people should be allowed to work more hours if they want" (because even if people are on average less productive working past 40 hours a week, some might be able to cope).
I think it's wrong to claim anyone advocating a 4-day workweek must necessarily believe a company will have higher productivity.
The experiment being discussed here literally sets workers the target of achieving the same output as they previously managed in 5 days.
Sure, some people prefer 4 day weeks and happily take a pay cut in return and some people want government intervention to give them a better deal, but - unlike the 5 day week - there is an explicit productivity claim by many 4 day week advocates being assessed here
If the gradient of your input-to-output curve becomes negative and stays negative, and you're working less than your competitor, then your competitor will fall behind if they're working sufficiently far past the point of negative returns.
I'm pretty sure the gradient of all input-to-output curves becomes negative at some point, and don't see any reason why that point should be exactly 40 hours a week. It could be more and it could be less, and probably depends on a whole bunch of other factors, but exactly 40 hours spread evenly across 5 days seems oddly specific.