Sounds just like a TRADITION! But there may be some validity to it, albeit subtle. Why be worried about premixing juices if the will be mixed immediately in your gut? Here is my two cents...
straight green juice is quite bitter and can be pretty nauseating, but there is a school of thought that its very important for one to taste the medicine (or food) for it to be effective. In the context of this bitter juice it could stimulate a beneficial biological cascade, such as hormone releases, pancreas/liver stimulation, etc...
Another concern of hers is that fruit juice oxidizes quicker (or at least visibly) faster than veggie juices. So she may have been worried about the fruit juice speeding up the oxidation of her green juice. But I think this is not a huge issue, just the fact that one is consuming fresh juices is better than worrying about how oxidized it may become from the juicer to your mouth... Hence, her practice of swallowing the juice very fast. Juice would be best consumed more slowly to mix with your saliva and have an even greater effect on your biological cascade...but this would necessitate making the juice taste better so you would actually ENJOY consuming it....
I like to juice loads of veggies (I can get away with this technique, except with radishes) then blend with a little fat (nuts, avocado, coconut oil, etc...), lemon/lime and stevia. Fruit is just a filler and palate pleaser, its not necessary, and can increase the glycemic value. I like to balance sweetness with a few carrots, stevia and some berries. So practice balancing the flavors of your juices and you'll likely drink them more often and enjoy it!
The goal is fresh concentrated nutrients from veggies, so make it strong with them then add just enough sweetness to taste good
Add these ingredients judiciously to balance the strong flavors of greens and other veggies:
Fat (avocado, nuts, coconut oil, yogurt, kefir, etc...)
Juice to the People!