They are two separate clauses i think

1. cardboard causes no problems

2. the cribs help prevent SIDS

I did a quick search and found this:

https://www.npr.org/sections/health-shots/2017/03/26/521399385/states-give-new-parents-baby-boxes-to-encourge-safe-sleep-habits

So its not about the cardboard, its about the makeup of the crib itself

I think he meant having a crib helps, not it being made out of cardboard.

Babies like pretending to be homeless