Well, vapor pressure is inversely proportional to IMF (intermolecular forces), which is directly proportional to boiling point, so a substance with a lower vapor pressure will have a higher boiling point.
Lower VP = higher IMF = higher b.p.
Normal boiling point is defined as the point where vapor pressure is equal to atmospheric pressure, so with a lower atmospheric pressure a lower vapor pressure is needed to "boil."
Normal b.p. = (VP = atmospheric P) so therefore lower atmospheric P = lower VP to boil = lower b.p.
I believe your statements are correct.