It does saturate at some point, though. If you're turning patients away who are in need of ICU treatment (as some Italian hospitals were), your ICU admissions will be constant and equal to your rate of release from ICU, so it will appear that you've "flattened the curve" even if the number of sick people continues to grow exponentially.

True, the paper talks about patients needing ICU, if you can get that statistic instead.