This is not true. What Humanae Vitae says is:
" With regard to physical, economic, psychological and social conditions, responsible parenthood is exercised by those who prudently and generously decide to have more children, and by those who, for serious reasons and with due respect to moral precepts, decide not to have additional children for either a certain or an indefinite period of time."
Prudently and generously are not adjectives to compliment those who have more children. Having another child must be rooted in the virtue of prudence and out of the generosity of our hearts. And those with serious moments may decide not to have children for a certain or indefinite period of time.
What NFP does is give us a greater ability to understand the moral weight of our sexual choices in marriage. Our consent to pregnancy must include an awareness of the chance of pregnancy.
As such, if I’m having sex after my period but before my fertile window, I know my chances of pregnancy are unlikely but not impossible. If I have sex during my fertile window, I know my chances are very high (unless we have infertility problems), and if I have sex during the period after ovulation and before my period,I know that the chance of getting pregnant is near non-existent.
This doesn’t mean NFP is always this straight forward. The postpartum period is one huge pain in the butt that is under researched. The overall probability of pregnancy over the course of one year is higher than when a woman is cycling because couples are more likely to use the fertile time due to prolonged periods of abstinence caused by false fertile signs you have to abstain through anyone because you might ovulate and might not. In the meantime, the research on NFP in general is all moderate to low quality. There was just a report on this recently. We need higher quality studies to gain a clearer picture of our actual risk.
But the more information we have, the more we are able to practice prudence. And this is contrasted with the unchaste nature of non-hormonal contraceptives, and the disrupting of healthy bodily functions to enable greater freedom with sexual activity without the consequences.
What the Pope rejected from the comissions recommendation was only one part. He rejected abstinence as an immoral means to prevent pregnancy. As such, the proposal to argue that because NFP was approved, contraceptives should be because abstinence in marriage was a negative. It was almost a proposal for something like a just war theory for contraception.