Were people really as haphazardly *burned at the stake* back in the day in Europe as they make it out to have been?

The body of the question seems to be very different from the headline. You do not seem to be raising any substantive doubts about any particular historical account. The article you link to about the Almarician's states that 10 people were burned at the stake in Paris c. 1210. I see no specific reason to doubt that this occurred. The Wikipedia article "Death By Burning" shows that this was a widespread practice within and outside of Europe over many centuries.

What you seem to be asking is something more like, "how could people be so cruel and sadistic?" That is a very different question, very open-ended, but I'll point you toward a few books that deal with this question in different ways.

In this excerpt from Discipline and Punish, Michel Foucault draws an interesting contrast between two moments. In 1757, a convict was publicly tortured and dismembered in Paris. Less than a century later, we had prisons that ran like factories. It's well worth reading that excerpt as well as the book, but I'll draw your attention to the last few sentences.

Punishment of a less immediately physical kind, a certain discretion in the art of inflicting pain, a combination of more subtle, more subdued sufferings, deprived of their visible display, should not all this be treated as a special case, an incidental effect of deeper changes? And yet the fact remains that a few decades saw the disappearance of the tortured, dismembered, amputated body, symbolically branded on face or shoulder, exposed alive or dead to public view. The body as the major target of penal repression disappeared.

In other words, cruel and public capital punishment is a common occurrence in many societies. It is only in the nineteenth century that more modern modes of punishment started to take hold.

Foucault analyses modern modes of punishment as a panopticon. We police our own behvaior to a great extent because we are certain that if we break certain laws, there is a high chance we will be punished. If punishment is more certain, it need not be so cruel. But in medieval Europe, there were no police keeping watch on the population. Punishment was uncertain, so it had to be cruel in order to be effective. The Church needed people to fear that God was watching them and would punish their sins. Burning at the stake was a visual reminder of what awaited sinners in Hell.

Another book that puts these kinds of changes into an even larger context is Better Angels of our Nature by Steven Pinker. Pinker is a cognitive scientist, not a historian, but he does look at a lot of historical data to show that violence in general has declined over time. The most relevant point he discusses is how state authority became more centralized in what is known as "the Civilizing Process". Homicide in general and cruel capital punishment in particular both declined as states consolidated their power over society and developed the capacity to maintain order through other means.

I've focused on the idea of punishment, but there are other ways to approach this. I might come back and expand on these a bit if I have time. One is the question of religious violence. It is relatively easy to convert from one religion to another (easier even then learning another language) and so religious identities are arguably the most easily threatened. This may encourage violence. The other angle we could expand on is cycles of violence fueled by materialistic opportunism. Some have argued that in specific times and places where witch hunts and the like took hold, people were in part motivated by opportunities to acquire other people's property by getting them executed. This clearly wouldn't apply in all historical cases but it may be important in some of the worst cases.