HOWEVER... she told me that school might always be a major challenge for DS. His level of intelligence (and, again, I'm skeptical that she could really thoroughly evaluate his level of intelligence in the hour that she had with him) and his personality (strong-will and self directed) might make it extremely difficult to find a school that will work for him.
Difficult isn't the same thing as "no school will work" for your DS. Yes, it likely will be difficult. I will even go so far as to agree that "no school is likely to work for him" WITHOUT ACCOMMODATIONS. Here is where you come in as parents. You will be advocates and you will work with the schools to try to meet your kiddo's needs. Difficult? Yes. Impossible? No. And depending on where you live, there may be options in different school settings. And homeschooling is a lovely option, if you can swing it.
We were told the same thing by our DS's tester. We were also told that at some point our DS would need to skip a grade, even if he was in a program for GT kids. And it proved to be quite true. We worked with our local school the spring before kindergarten to get help getting a teacher who wanted him and who was good at differentiation. We worked again with the local schools to get a grade skip. Things probably would have been OK for a little longer, but it was still a lot of work advocating in our local district. Then we discovered an opening in a school for HG kids. With DS's grade skip, the accelerated program was perfect, and it's been great so far. The best part is that I haven't had to advocate for more yet, so it's been a nice little rest.
Others here have different paths, but the similar story of "it will be difficult for your kid to fit in". I would say that is true only if you do not do anything to advocate for appropriate materials for your kiddo. Do not despair! Even though it's hard to hear, it will be OK.