As instructed on the website we didn’t print anything out, so we just brought our passports and immigration was completely without any problems in Miami. Our passports also weren’t stamped as seems to be common now.

When we got into an immigration check near White Sands national park (closed road and checkpoint next to the road) the guards checking us were nightly confused that our passports weren’t stamped and we didn’t have a visa or any kind of printed documentation. And we were confused that we needed any of that?

One guard went to check on us with his computer, I guess, and everything seems to have checked out. So we didn’t need anything after all, it just seems that when you get into an immigration check those checking you might prefer to not go check with a computer, so printed documentation of some kind can get you going faster. (The guard also told me that we should have printed out documentation that we paid for ESTA?! Which seems confusing to me since presumably if we didn’t have paid we wouldn’t have been let in.)