IME when you login at most properties using your HH account, you will automatically receive the premium speed. You do not have to choose between standard/premium on a subsequent screen, it just automatically logs you in at the premium speed.

I've tested at numerous properties by putting HH credentials in on my laptop (and automatically getting premium), and intentionally using Name/Room # and picking standard on my phone. Speedtests on both have show that standard still clock around 1MBPS, premium is usually in the 3-5MBPS range.

This seems to be the case for the majority of the US locations I've tested. There do seem to be a few that will give a promo code at check-in, in which case I've just used the promo code.

I feel confident enough in the system that I don't bother testing my connection everywhere I go anymore.