Different children will react differently, of course.
It helped that I had read The Wasp Factory before becoming a parent.
If she is getting fooled that carbonated water is 'juice', then I'm assuming she doesn't know what juice actually is and therefore has no association of juice = sugar drink. So why the need to trick your daughter?
Couldn't you have just called it 'fizzy water', or if water is associated with 'boring', call it 'fizzy drink'. She'd still get it from the bar and have the excitement of that.
Sounds like you parsed it just fine. It was just an error in the actual logic.
All of these are terrible for teeth because they're high in sugar and they're sticky, and there's guidance to avoid these things.
Also, dental health isn't the only reason to minimise sugar intake.
Tooth extraction is the leading cause of child hospitalisation in the UK.
A few of those children will have problems such as hypomineralisation, but many extractions are entirely preventable with better diet (milk or water to drink, not fruit juice or sugar sweetened tea or soda, and especially not in a bottle or sippy cup) and better oral hygiene.
And it's important to start these habits early.
https://www.theguardian.com/society/2016/feb/27/england-hosp...
https://www.theguardian.com/society/2014/jul/13/teeth-proble...
http://www.nhs.uk/Livewell/dentalhealth/Pages/Careofkidsteet...
We soak them in lemon juice to keep them from turning brown while dehydrating, but since he loves lemon juice (and will drink it out of the bottle if we leave the fridge unlocked), this is a pretty huge selling point for him.
Further down the road, you presumably don't want to have a kid that needs to wear expensive clothes to school to feel accepted. And when they are that age, you can't convince them that less expensive clothing is expensive too.
It's cruel to expose children to pain and harm, especially when it's normally completely avoidable.