Looking at Texas Medical Center (106,000 employees, 10,000,000 patients per year, 9,200 hospital beds - a massive complex), they're reporting a big spike in hospitalizations for COVID-19. Does somebody have some kind of official documentation demonstrating that TMC is not actually seeing a rise in COVID-19 hospitalizations?
Here's what they're reporting: 
(Source: https://www.tmc.edu/coronavirus-updates/tmc-daily-new-covid-19-hospitalizations/)
Clearly that number is going up. I don't have any evidence to say their numbers are wrong. Here's their current forecast for total beds used by COVID-19 patients for the next two weeks:
On its surface, that seems like they're seeing a jump in hospitalizations with an expectation that it's going to continue for at least a couple of weeks.