Attempting to reverse the burden of proof. (And I think you must mean "any other studies".) In general the burden of proof is on he who asserts the existence of something, not the other way around (which leads to all sorts of contradictory outcomes). Those who assert that coercive lockdowns help with suppressing the spread of Covid-19 have the burden of proving that it in fact suppresses it.
The only reason to think they might work is that in the limit extreme social distancing has to work. But extreme social distancing and coercive lockdown orders as implemented in the US are very different things and there are plenty of reasons to think coercive lockdown orders might not work. There is also no available study, analysis or data to suggest coercive lockdowns have worked in the US for Covid-19.
It is of course strictly true that failing to disprove the null hypothesis (as in this study) does not prove the null hypothesis is absolutely true.
Nonetheless, I think it is fair to say that the balance of evidence presently is that coercive lockdowns are not achieving their intended effect.
I am however continuing to develop a more sophisticated test that would include time of implementation and the full time course of the cases and deaths to see if that might show some sort of effect of the coercive lockdowns.