Yeah, the fruit avoidance IS the fructose. They will eat it, but only alone and on an empty stomach. They also don't eat avocado, squash, carrots, potatoes, sweet potatoes, etc. The idea of the diet is to prevent the body from being able to absorb any fat by completely forcing your insulin to never spike, and if it does spike, have nothing else to 'feed' the fat. So fruit would cause an insulin spike, so eating anything with fruit would cause weight gain.. And then all the other weird mixes they aren't allowed. Makes it tricky for my picky eater of a mom. Not to mention they just get lazy and just don't buy the stuff. I haven't seen my mom touch a fruit in about 2 months now.
Wow, I think your parents should look a little into fat metabolism and the role of insulin and less into what is it Suzanne Summers? has to say. Fearing the GI and "insulin spikes" is just silly (unless your diabetic of course).
Fruit is very nutrient dense and do they realize how much actual fructose is in a piece of fruit?
Here is a good read for you on fructose:
http://www.alanaragonblog.com/2010/0...tose-alarmism/

Overall I think you have the right idea and if you throw in some exercise you should be well on your way. Good luck and Happy Thanksgiving!