Because I'm such a *sensitive* guy I recognized right away that the problem was she didn't want to drink the water at all, not that she was worried about running out. All this is inextricably tied up with the romantic issues, so our advice on here is a bit like the Car Talk guys on NPR giving romantic advice.
But since that doesn't stop them either … I'd say buy her a sawyer mini, and include as much technical info that they put out as you can to convince her it is safe. That way at least the rational part is taken care of – that should get you about %10 of the way there :-)
Like craping in the woods, doing it the first few times with nothing untoward happening is probably enough to get her to relax about it. One of the benefits of backpacking is to spend some time pealing away our artificial layers of socialized anal retentiveness regarding comforts of home. Some people have very hard time doing this – I want to say for some it is impossible, but I have no evidence that is the case. One interesting thing I notice is that after a week or so craping in the woods, I am very repelled by going into most bathrooms for a while, especially if it is a port-o-potty in a regular campground. So that is an interesting inversion that can happen. When this type of thing finally hits here the "problem" will take care of itself. But as others have been saying, hitting her over the head with it yourself is usually counter productive.
I'd say that the good news is that she apparently likes you enough to put up with the the backpacking (and the extra weight). If it were me I'd let her be if you are smart, and just go on GF trips and "regular trips" sans GF – each with a separate mindset.
Some might say I should talk, as I think I mentioned some weeks back somewhere on here that I once knew a particular woman was not for me when she was freezing and wouldn't put on the long underwear bottoms I offered her because there were men's style. This was just a subtle feeling, but after that in retrospect I knew that was the crucial moment.:-(