I completely understand why that story has rattled you, but the experience of dozens of people on this thread who've been advised to say nothing and haven't come back to complain about duff advice - indeed some have come back to say it all went smoothly - suggests that you'll be fine.
I got a whiff of that article not being quite 4 beats to the bar, something about a rather carefully worded denial by one of the party, which makes me think that there's more to that story than meets the eye. I wouldn't be surprised if some idiot said "werl, I was only ARRESTED, they can't touch me for that" , and dropped themselves in it that way.
If you are not on a watch list, don't make things complicated and draw no attention to yourself, they just don't have the resources to dig deep into everyone's past. Answer questions briefly and directly (if not honestly) and be exactly what you are - a family off to have a lovely and well deserved holiday of a lifetime, hold your head up, and smile, and you'll be fine.