I use that site only when I can't find a primary source or a more reliable source such as a reliable Visitation or the Plantagenet ancestry book.
Botsford came to Milford, CT which is an early community I have done a lot of tree building for since so many of my ancestors lived there and were among the founding families.
http://www.botsfordfamily.org/downloads/PedigreeChart.pdf
It looks like the Botsford research supports Alice's mother's maiden name being House.
I would prefer this site and this pedigree chart over the first source.