Yes. Private schools are known for this. It does matter if someone's grandparent attended a school, even if it was decades ago. That doesn't mean that the college applicant isn't also qualified to attend the school (which is what BK was saying - I don't doubt that he did work hard to get into Yale), but legacy is definitely something admissions notices.
Has it been absolutely confirmed that his grandfather attended? Seems like a strange thing to lie about.
jmo
Can't post links from my phone, but multiple news sources published about Legacy yesterday, even providing his grandfather's full name. Newsweek , for example, which I would hope isn't yet considered a far left wing fake news source?