This is not true. If the problem statement itself is a unique creation, and the solution is publicly viewable and gives details on the question itself, the question writer may have the copyright even if you signed no NDA when solving it. Even if not, if a company wants to sue you to try to keep their interviewing IP private (as they see it), they can tie you up in court at a trivial cost to themselves but a life destroying cost to a lone developer.

Source: I once had a dragged out legal dispute with a company that used a GitHub DMCA takedown to tell me to remove a public repo in which I solved their takehome challenge (I had signed no NDA or otherwise any type of agreement of any kind prior to solving it).