Do you think you don’t know know your children very well because you send them to school all day and don’t homeschool them?!
Whatever the rights and wrongs, I don't think you can fairly compare the two scenarios. It's the norm for most people over the age of 5 to spend hours each day away from their family, be it at school or work; but they categorically live in one place, which is usually the same place as the other members of their nuclear family live.
Ask a boarder where they live and some might say their home address (with their parents), some might say their school, some might say both and others might hesitate before giving their answer. A child going to 'normal' day school (whether state or private) would instantly and unequivocally say their home with their parents.
I get that the holidays are longer, but children in a 'normal' school regime also have weekends and holidays between terms. Nevertheless, if you asked them "Are you a schoolboy/girl?", it wouldn't occur to them to say No, merely based on the incidental fact that they don't have to go at weekends or in the holidays - yet it's those incidental weekends and holidays (albeit a few weeks longer over the year) that parents of boarders are seizing on as 'justification' (if any were needed) that their children 'aren't really away at school all that much'.
I realise that plenty of parents disagree with me, as they have every right to do so, but I don't see why you'd cling on to those weekends and holidays when you get to see your kids, when you could have those plus the majority of hours every single day as well.
Maybe it just comes down to priorities and what you believe is most important for your child. I believe that growing up as part of a family where you spend time together every day is the main priority and then education/socialising with peers, whilst also very important, comes a definite second. Some families seem to make their children's best-possible education (which some perceive as being achieved by boarding) the main focus of their children's lives and then work their family life around that.