If I had a camera in the LPS the other day I would have video taped the sad sad existance of a betta in a vase struggling to the top around the damn bamboo just to breathe.
If that doesn't convince her that she is wrong then I suggest she not obtain a live fish. Fish are live creatures with their own needs and specifications. I think it is a little ignorant and unfair that she would be so insistant on getting a vase. If she wants a vase then let her get it, but don't let her put a live animal in there!!
The problem with bettas and vases is that they require a wide surface area in order to breathe. The taller and narrower the tank the harder it is for them to breathe. The longer the better. It's just an absolute requirement for the fish.
This fish is pathetic. Suer it got its color back but he is so listless. I know with time he will earn to live well... I didn't listen to the commentary but I'm sure you should show it to your wife. Also the before and after pics.