There's a long history of society deciding "how other people should raise their kids". If you believe the studies that show these results are BS, then you probably have no real credibility to evaluate your own reactions or your child's to "punishment".
Why is there embarrassment? And are you so sure the first reaction is a logical connection to one's behavior? I got hit with a strap, bare-assed as a kid, and yes, I consider that sexual abuse. Because it is. Not that my Dad was a molester; he was a great guy, I trusted and still love him. But A + B = C. It's abuse that's sexual in nature, therefore, it's sexual abuse. Because sometimes the "spanking" was enraged, disproportionate, and seemingly random, I went a long time, as a kid, not understanding why I was always in trouble at school, and around authority. It was beneath my parents to explain themselves to me, because a parent doesn't have to explain themselves; the kid should respect the parent, and it's nobody else's business, anyway. Sound familiar?
I think a big part of this disagreement is crossing the line of "if this is abuse, then my parents were abusers". One can still admit that one's parents did something unhealthy (which was/is accepted and legal), and still love, understand and respect them. There is no dichotomy.
If you give your kid a swat or two because he won't stop acting out, sure, that's still legal. It's also legal for some of us to think that's very unhealthy, express that, and try to change the law to reflect current, societal thinking.