I actually agree to a certain extent, the healthier options can be more expensive.
Example:
Chicken breast 500 gr (17.6 Oz),£ 5.00 -
minced beef (high fat content), 500 gr, £ 0.99
cheap microwave meal, £ 0.99
So for my £ 5.00, I would get 2.5 kg of fatty minced beef, enough for burgers for a week. Or 5 microwave meals, which would last for the week as well.
Even worse when it comes to fish, 500 gr of salmon are about £ 8 - 10. I love fish, but unless I find an offer, the only fish I get is canned tuna. I tried going for the fish from the 'reduced' shelf last week, and I am still struggling to keep food down at the moment. Not a good idea. 
White rice, 500 gr bag, £ 0.69 - Brown rice, 500 gr bag, £ 1.99 (both supermarket's own label)
White bread, 1 loaf, £ 0.45 - Multigrain bread, 1 loaf of the same size, £ 1.49
You get the idea.
Granted, it doesn't go for everything. If I buy 5 bars of chocolate, it'll cost me about £ 6.50. For that, I can get a bunch of bananas (£ 1.00), some apples (£ 1.00), nectarines (£ 1.00) and usually some berries, if I get them on offer.
That said, blueberries and raspberries are between £ 2 - 3.00 for a small pack, which lasts me two days. Not a lot, if you think about it.
Water - would be nice if I could drink the tap water here, but I can't. It's full of chlorine, and has a horrible smell, a mix of chlorine and mould, to it. Even a water filter couldn't get that stuff to taste even remotely like water. And the cheap stuff out of the supermarket tastes exactly the same, so in all actual fact, my water is more expensive than my husband's Pepsi.
I have to say that since I tried to start eating healthier, my grocery costs have gone up significantly, but mainly because I have to buy my healthier options on top of the junk that I have to buy for the rest of the family. That's something that needs to be taken into account, people who have a family that might not be interested in the 'rabbit food' (his words, not mine) at all.
And another problem for me is that I can't buy any fruit or vegetables in large quantities, and even if I buy a smaller amount, half of it goes bad before I can eat it. I don't have the time to go shopping every other day for fresh stuff, so I am spending a lot of money on things that go into the bin after 3 or 4 days, which annoys me to no end.
But yeah, I can imagine that if you only have to go shopping for yourself, or if you have a family that agrees with the healthy options, after a short while you would be able to save some money. But in a less ideal situation, which is probably the case for the majority, the healthy stuff will go on top of everything, and strain the budget.