I the example you cited, the author said she saved a lot just by not going to fast food restaurants. As these costs include service (which you don't have to pay if you cook yourself), it's not the cost of the food which is lower, but the cost of you overall style of life.
I could say the same thing as our son (4) is on a gf/cf diet: We spent more on food, but we spend much less on restaurants so it sort of balances out. If we would attend restaurants which offer high-quality-gf/cf meals we would be poor by now.
You get the financial advantages of not going to restaraunts and takeaways by simply avoiding them - you don't need to take up the GF/CF diet. I'd also carefully look at how it impacts upon your health too, with any exclusion diet you run the risk of deficiencies.
I went GF for a week (my gastro wanted me to see if i was gluten intolerant) I stopped...I missed my Oreos.
But it was only a little more expensive...not ungodly so.