Essentially, the exterior crust and the interior evenness are both side effects of the distribution of water.
The Maillard Reaction - the chemical reaction responsible for the brown crust - happens at about 150° C. Generally you're baking at a much higher temperature than this - say 200° C.
The first question one might ask is, why is the crust only on the outside? And the answer is because only the outside gets dry enough; as the small amount of water on the surface evaporates, the temperature is allowed to rise to ambient oven temperature.
The reason it doesn't happen on the inside is precisely the opposite; water boils at 100° C, so as long as there's still water in liquid form (and bread is, to a large extent, water), the temperature can't get any higher than that. The interior of the bread is always regulated at approximately 100° C, and since the baking temperature is uniform, so is the finished product. It's almost like poaching an egg or a piece of meat; no part of it is able to get any hotter than the liquid around it, so the longer you cook it, the more uniform the temperature gets.
If you continued to bake the bread until all of the interior water evaporated into steam, then it would eventually start to undergo the same process as the steam slowly escaped. But we usually don't bake bread that long, so it doesn't happen. As commenter Ray points out, there are some types of darker bread such as pumpernickel which involve intentional "overbaking", but obviously not to the point of burning it.
Note: There may also be a certain element of the process that is due to steam being trapped inside; the water vapor, like any gas, expands and distributes itself fairly uniformly throughout its container. However, the bread is porous, so this steam eventually has to escape; if it didn't, you'd end up with a very damp interior after cooldown from all the condensation. If you measure, you'll also notice that the weight of a fully-baked bread is about 10% less than the original dough weight. So the steam doesn't stick around indefinitely, but the continuous evaporation coupled with the temperature self-regulation (due to the boiling point) keeps the temperature relatively constant.
Three reasons come to mind why your bread may have turned out too hard-
1- If you didn't let it rise enough.
Flat breads often don't have a proofing step. The dough should double in size on the first rise and then after you divide the dough let it rest to make rolling out easier.
2- Working the dough too much without resting.
When rolling or stretching the dough be gentle. You don't want to force all the air out. If you do think that you overworked it, letting it rest for a while will let the yeast work a little more.
3- Too low of oven temperature
Traditional flat breads are often baked in large, wood-fired, brick ovens. Your recipe calls for 475F and I would say that that would be a lower bound. Since flat breads are so thin they dry out quickly. In general the hotter you can bake them the better. Try throwing a couple loaves on a very hot grill but indirect heat. Expect this to take less baking time than your recipe. If you get some charring that is ok and even desirable. If you get charring that goes all the way through then you rolled the loaves a little too thin.
Personally- I am skeptical of the milk basting. This would keep the surface of the bread moist but it would cool down the oven which would be horrible for the bread. I never saw turkish bakers basting their flat bread but maybe it is a regional thing.
Best Answer
I'm not certain from the question about what "doneness" means. Is the bread still "raw" inside at 95C? If so, I'd guess something is wrong with the calibration of the thermometer.
Failing that, my guess is that this has to do with either various other external factors (e.g., the bread may be "set" inside, but the exterior is not browned sufficiently, or the crust dried out enough) and/or things having to do with moisture.
Once you get to 95C and above, the structure of the bread is definitely set. It's not going to collapse if you pull it out of the oven. It shouldn't taste "raw" or overly "doughy" inside. The bread should be "done," at least in the sense of fully cooked.
But to my point about moisture: what generally happens to bread once it reaches a high internal temperature is that the internal structure gradually dries out. It takes a long time for moisture to migrate out from the center and through the increasingly hard crust. The interior of the bread will change from a spongy and "moist" texture to an increasingly dry and stiff one as time elapses in the oven. The retained moisture when the bread is pulled from the oven also can have significant effects on the outcome: a dough that is very moist before bake and which doesn't expand much will often remain moist internally, and that moisture will likely rebalance itself during cooling, some of it going to the crust, which will soften. If you want a crisp crust, you'll have to bake longer.
Some of it may have to do with the recipe. For example, a quick hot bake may give good oven spring, but may not allow sufficient time for moisture migration. So a crusty bread baked too fast may display a high internal temp, but then soften as it cools. Turning the temperature down during the bake may allow for the desired texture with a longer bake (and without burning the exterior). If your bake time is off from the recipe, the internal temperature may not be as reliable an indicator.
Some of it may have to do with loaf and dough characteristics. As hinted above, oven spring and size of holes inside the interior plays a significant role in how moisture migrates internally. If your bread isn't rising as much as the recipe assumes (or rising too much), you might need to change your bake time/temp as well as your assumed final interior temperature for the loaf. Extra humidity absorbed or lost due to kitchen conditions at different times of the year can also play a role -- I've baked the same recipe under different humidity and temperature conditions with precise measurements and gotten significantly different results.
Lastly, of course your personal taste concerning doneness may vary from the person who wrote the recipe. Sourdough breads can vary inside from everything from a kind of "creamy" and somewhat moist interior to a very dry and tough/chewy interior. Personally, I like the former, but if you like the latter, maybe you are most satisfied with a result different from the one the recipe intended.
Bottom line is that internal temp is a guideline just like anything else. But I personally have found it more useful than other guidelines (like the "hollow sound" test, browning level of exterior). You may need to tweak according to your own experience and preferences.