I think you've misunderstood what they're suggesting - they're considering the transfer from parent to child to not be a realization, so there's no taxes, and no change in basis.
The child who sells the house, then has to pay gains from when the house was first purchase, rather than against the value when they inherited it
The child who sells the house, then has to pay gains from when the house was first purchase, rather than against the value when they inherited it