It seems as though engineering is the fourth most trusted profession behind nurses, doctors and teachers. About right? http://www.imeche.org/news/news-article/engineering-'is-the-fourth-most-trusted-profession-in-the-uk
Engineers are accountable to courts of law for their actions and technical decisions, so they are by definition responsible and trustworthy persons. This mentality is infused to us when we study engineering, as the people who design and build bridges, for example, must make sure that the safety aspect is secured. Now, if you add to that the fact that most of the large-scale projects are carried out by teams of engineers... I mean, it's easier to trust a group of people than it is with one person.
Engineers are also human and are prone to making mistakes. Difference between a mistake made by an engineer and one made by someone else could be that a mistake made by an engineer could cost someone their hand, eye or even worse, their life. That is why engineers learn to be more careful at what they say or do, how they handle situations and how they react to their surroundings. Engineers pick this up as a trait when they are working. But work life and private life is somehow interconnected (in certain ways). So, they start applying these rules in their private life too. However, I think in the linked article, the people think engineers are more trustworthy because this is one of the professions that require high level of education. Educated people are usually respected and trusted more than uneducated people in some parts of the world. At least, that’s how it works back home for me.