It's important to note that there are intersex conditions where observation is not as straightforward as usual. It's also important to note that the brain is part of the body, and at least some instances of trans identity seem plausibly due to intersex brain development, further complicating the issue (even though "intersex" is usually taken to cover "body not including the brain")

In these cases, the "assigned" terminology may occasionally be helpful. In the usual cases, it's an (accurate) observation, not an assignment. People are not assigned 8 lbs 2 oz; it's a measurement.