I've read somewhere (it was a vanilla cake recipe, IIRC) that 3/4 cup yogurt plus 1/4 milk is buttermilk. A recipe (buttermilk biscuits) calls for buttermilk and I'd like to know if I can use this formula to make buttermilk.
Technically, this is not precisely buttermilk, but it's pretty close in both composition and usage.
The term "buttermilk" can actually refer to a wide range of fermented milk varieties. Traditionally, buttermilk was produced by allowing natural bacteria present in cream to ferment some of the sugar lactose into lactic acid. This made churning butter from the cream easier and also helped protect the cream from spoiling. After the butter was churned and removed, the liquid that remained would be your buttermilk (today referred to as "traditional").
Nowadays, mass-produced "cultured" buttermilk is produced by taking pasteurized low-fat milk and introducing bacterial cultures to produce lactic acid in a similar fashion. That's similar to how yogurt is produced, but yogurt is generally allowed to ferment for longer until the milk proteins set and thicken. There are many varieties of yogurt with slightly different cultures from each other and from cultured buttermilk, and the beginning fat content of the milk can differ too.
So, technically these are distinct, but if you use milk to thin out yogurt, you're producing a beverage that (like buttermilk) contains lactic acid, producing that distinctive tangy flavor, and which (like buttermilk) is somewhat thicker than milk. Your identified ratio is the same as other recommendations that I found while searching around, so you can definitely use this to substitute.
Yogurt and milk are not buttermilk. Buttermilk is actually the liquid you have left over after you've made butter.
Generally, in baking, it's used for its acidity and protein content. If you want a viable substitute, milk and yogurt can work, or milk and some lemon juice. It's a good idea to let these mixtures sit a bit after you've combined them, to allow the milk to curdle and acidify.
If you were to make butter at home, one way to do so is to inoculate some heavy cream with a yogurt culture. This introduces bacteria into the cream which will acidify it and cause the fat in the heavy cream to glom together more easily.
Once you've fermented the cream as you would ferment yogurt (in a warm place for about 4 to 12 hours), the result is something called creme bulgare. This is similar to creme fraiche.
If you churn the cooled creme bulgare, you will cause the fat in it to conglomerate through mechanical action. I use a food processor to do this. You process the creme until it separates, you'll clearly see the butter clumping together and a liquid separating from it, this liquid is buttermilk.
To finish off the butter, I strain the mixture, save the buttermilk, and cool the butter until it is no longer soft. Once it's not soft, I put it in cheesecloth and squeeze the remaining buttermilk out of it. Squeezing the buttermilk out of the cooled down butter is much easier since the butter will not be able to pass through the cheesecloth. Additionally, it's a good idea to do this since it ensures the butter last longer.
I can't find "buttermilk" anywhere in the recipe link that was originally referenced (http://parsleysagesweet.com/2013/05/18/tourte-milanese-a-meal-en-croute/).
Regardless, the information you presented in your post seems to refer to "cultured buttermilk" and not "the milk left over from making butter."
If the yogurt you're using has active cultures (look at the ingredients list), then the yogurt/milk (whole milk) mix will result in something reasonably close to "cultured buttermilk" in flavor, body, and acetic enough for activating baking soda if your recipe calls for that.
Yoghurt + Milk != Buttermilk.
It is made by shaking Cream as long as possible. The first you'll see in this process, the Cream will become whipped cream. If you keep on shaking, the water and fat will separate from each other. The fat will agglomerate and is further on called butter.
The separated water, the leftover, is called buttermilk (traditionally).
The mixture you mentioned is somewhat cultured buttermilk with some substitute for the removed fat and stuff which makes it less liquid and regulate the acidity. Some more information can be gained here:
My guess it, that the recipe is meaning a cultured type of buttermilk, because most people would associate buttermilk with cultured buttermilk as a replacement to the traditional meaning.