If we explain everything using the example of the psychology of human relations, then the presence of open source code for an application is about the same as the sincerity and openness of the person with whom you communicate.
If during communication you see that your opponent is sincerely disposed towards you, is open and does not try to hide something from you - your degree of trust in his direction increases, since you perfectly understand that nothing unpredictable should be expected from such a person.
"Closed" people who seek to hide something during a conversation, or those towards whom you feel obvious insincerity, - in this case you will always feel stressed because you will not know what to expect from such a friend.
This is a pretty simple but straightforward way to explain why people are more likely to trust open source applications.
Openness is synonymous with the sincerity of developers towards their customers. And now it's an unofficial "rule of good manners" for all developers - open source is the ability to attract the same open-minded people.
Thus, a healthy ecosystem is formed around the one who professes such principles.