I would read the entry for baby John as you have.
Although being cared for by the Henerys he was not
a grandson--- the enumerator will have looked at their daughter & perhaps made an assumption & so
Daniel Henery miust have been saying "not family ".

In a later census John would probably have been
entered as "lodger " / "nurse child " or even "adopted"
long before this was legally possible as happened in my
family which took in an orphan baby.