At what point does a PhD student have to commit to a research group (US)?
This can depend a bit on field and even by institution. It would also make some difference if you are applying with a BS or an MS already in hand. If you are early in the process then the early part of the doctoral program will likely involve advanced coursework, so choosing a specialty can typically be put off. 

But starting later, ready for research, it will probably be an advantage to know, going in, which group (or groups) you are most compatible with. 

But overall, your assessment in the question is correct. People choose a bit later than first contact and some people change. In math, for example, there is less reason to choose early than in, say nuclear physics, where expensive labs might be part of the process. 

I changed groups because I changed institutions. The old situation didn't work out for me. I joined the new group relatively soon but held an MA at that point and knew who I wanted to work with. But it wasn't a choice made in the first weeks.