I am not sure where this rumor came from, as I have never heard it. But, the post-civil war population explosion can be explained succinctly by two factors:
- Peace. With the consolidation of the continental regions came a new peace that replaced nearly 50 years of warlord driven unrest. The first 10 years of the PRC were successful by nearly every measure. Manufacturing, agriculture, warfare, etc., everything was coming up roses for the republic. Stability and success means population growth.
- Health care - Mao and the party focused intensely on improving public health. Throughout the 50's and 60's China improved health outcomes and reduced infant mortality, which is the most likely reason for the dramatic increase in population. As fertility rates fell, the rate of growth naturally declined, with the one-child policy contributing to even slower growth. But that is a different story.
The rumor you reference is more politics than anything else. The government did not force families to grow. The fertility rate did not change at all in the first 15-20 years of the PRC, but the health care improvements meant more children were surviving to adulthood, and that makes all the difference needed for an explanation.