Does toasting and grinding whole spice really improve curry flavor?
I don't think roasting spices "improves" them or rejuvenates stale spices but it certainly does change the flavor profile in ways that may be desirable in some cases, for some spices, less so for other spices in other cases. This is common sense to me and also what I got out of the article. I think the heading of the article is too absolute for the content.  

Whether or not dry-roasting is "better" depends on which spices and what you are doing with them - how long they will be in the recipe, what else is going in, etc, and what flavor profile you are looking for. I think the article goes into a lot of detail about this and has some good references (it looks like an interesting blog, thanks for sharing.)

For example, fresh, dried coriander seeds don't taste the same as toasted coriander, and fresh, untoasted, whole cumin doesn't taste like toasted/dry-roasted cumin. 

If you add it raw vs dry-roasted, in general you are going to impart a slightly different flavor profile to the dish. Some recipes are complex and/or delicate enough that this matters, and as the article notes, this will be specified in recipes from trusted sources. 

If you are making an uncooked chutney that you want to season with coriander seeds or fenugreek seeds, you need to toast them before grinding them if you want them to taste cooked. Or if you are seasoning your raita or lassi with cumin, it will probably taste better (or more like what would be expected) if you toast it.

But "better" really just depends on what you are looking for. The author of the linked article talks about what flavors she wants to impart to her squash soup, and that is great. If it's her recipe and her tastes, she should make it how she will enjoy it. But if you are trying to replicate a traditional recipe, you may want to follow the traditional methods for that dish at least the first time you do it, which may or may not use the spice how you are used to using it, it's even possible that the traditional way won't taste as good to you as using them how you're used to. 

So again, that's fine, adapt the recipe, with the understanding that it may be a bit less traditional. That's how we end up with fusion cuisines, like Indian-Chinese, or British-Indian or American-Italian, adapting traditional methods to new ingredients or to differing tastes and preferences.

For the most part, in my Indian cooking, I rarely toast spices before adding them in unless I'm making something where it isn't going to be cooked further. I hadn't heard or been told that you "always" should roast all spices before grinding them. 

In fact, most of the Indian cooks I've learned from use pre-ground spices for convenience, and I sometimes get weird looks from people in my generation when I make things less convenient and start from fresh, whole spices instead of spice blends. My point here is that there is sometimes a difference between what is ideal for a dish vs what is ideal for daily cooking. Both the daily "easy" method and the for-special-occasions-only multi-step preparation can be equally traditional for what is ostensibly the same dish.