I think I may have an answer for you on "morals" being included in Google's definition. In my piece, I wrote about how those with little to no integrity, like Google, will try to make integrity have multiple meanings. It's a method they use for "watering-down" meanings they want to make debatable, that never have been, until now.

For example, if you define integrity as being even partially based on "morals," then it could be said that even the most despicable scammers in the world have a "level" of integrity, because they followed their personal moral code. It looks like another attempt to change the true meaning of a word to include more unworthy types.