I think it means nothing at all:
100% Juice
with other added ingredients
I think I agree.
I also think that the juice bottling company doesn’t understand what the term “one hundred percent” means. 
–James
I think the juice company knows exactly what it is doing. They know that people are being educated on what to look for in their food. 100% juice not from concentrate is the lesson being taught to be better for you. People are being primed to this lesson. So this juice company is hoping to trick people who might foolishly only read the big print and ignore the little print.
Obviously, this juice company are cheats and crooks and all their products should be avoided.
djm
Or doesn’t care.
Probably the same as “Made with 100% real juice”.
Which means that the total product likely contains about 1% juice if that, i.e. one of the ingredients is 100% juice.
As the effective intelligence level of the public continues to decay, you can expect to see more and more disingenuous advertising like this to pop up.
We have a natural food store nearby called “As Nature Intended” with an orange juice squeezer.
You pay about £4.50 for a litre of juice, and set the machine going to juice as you watch.
It’s pricey, but the best and freshest juice, a real treat not to be guzzling their “other added ingredients”.
They aren’t giving 110%.
It means “BUY ME!”
There are a few of us who are getting more and more intelligent as the general population becomes less so. It is “we” who are marketing the juice.
I must say I admire their confidence in their own ability to interpret Nature’s intentions. I’m very happy to learn that for all these millennia Nature was waiting for electric squeezers to be invented so that oranges could be consumed according to her designs.
Similar strange presumptions crop up quite frequently in advertising. For example, a phrase that struck me forcefully many years ago exhorted American tourists to “See Europe as it was meant to be seen…”
Meant by whom, I have always wondered.
That reminds me of some cereal Kellog’s put out a couple of decades ago. I think it was Mucus or Musilix or something. They said, “The way breakfast was meant to be.” Ugh.
I think, Fly, that was Mueslix, and it was supposed to conjure thoughts of a lovely, heart-healthy muesli multi-grain mix. But you’re exactly right about how it really sounded to the ear. Someone wasn’t on the ball in that marketing session.
And what on earth is a soup that eats like a meal?
I don’t know. How does a meal eat?
Something memorable. None of this happens by accident.
Darned space aliens again. 
Just what is juice?
It all depends on how you define juice.
One of Merriam’s definitions: “the liquid or moisture contained in something.”
Therefore, as long as there aren’t any “solids” (yuck) in the container I guess it could be advertised as 100% juice. 
I’ve always wondered about this:
If it really is clam juice then they must squeeze it out of clams… Or it’s the juice from their shells. Either way there’s more for you because I’m never going to try it.
It means, basically, that someone is lying. So common these days that there is little care to conceal it, it seems.