I'm pretty doubtful that there was a spike. The states like Texas, Florida, California, and Arizona have just been increasing gradually all the time. And NY didn't spike, even though there were protests. The national "spike" appears to me to be a phenomenon of adding up the individual states, where the declines were overtaken by the rises.

Do you/we have any good reason to believe that outdoor gatherings are much of a problem? The impression I've gotten is that indoors is where most instances of large amounts of people getting infected at once happens.