Bear in mind that if one login and password lets you get to both the password reset email and your SMS 2nd factor, you've turned two factor auth back into one factor auth. (So, then, turn two factor auth on your Google account...)
You are definitely right, but even though other accounts 2nd factor auth can be passed via password reset email, that would require a login to my gmail, but my Google account also has a two factor auth.
Edit: sorry for repeating you, I just show your footnote parentesis