It seems to depend on the person? I've seen some anxiety-prone friends freak out on thc, while others felt better like they never had before. It's weird!
Some people do not become anxious from cannabis, that is true.
The problem is recommending a drug with one of the most common side effects being anxiety to a person who has severe enough anxiety to have sought treatment for it and been prescribed benzodiazepines. While it might work it might also trigger a panic attack.