That is just plain FALSE on both points.
It is not a NEC requirement to get a permit for anything.
Governmental entities institute requirements that permits be obtained for certain activities. if the activity engaged in required a government issued permit and one was not obtained, than the law, ordinance, or rule requiring the permit be obtained was violated, not the NEC.
And there is certainly nothing inherent unsafe about unpermitted work. It is in general no more or less likely to be unsafe than work that is permitted.