All iOS users blindly trust that things will be OK. They have no other choice and Apple does a good job of filtering things in most cases. At the end of the day though there is no way users on that platform can exercise even common sense. You have no choice but to trust Apple. Google, on the other hand, does no filtering and lets users use common sense. Both approaches are flawed, just in different ways.
Because I do not know what happens when you seek app approval from Apple, I'll simply make a few guesses based upon what I do know. Last I knew, there was an approval process for apps and it was not a cursory inspection.
Again, I do not know what hoops devs must jump through to get his or her app approved by Apple.
But consider this:
The Apple/iOS sandbox provides very strict limit on the system resources applications can access. It is not a matter of blind trust. Programmers must write code that "plays" only within the sandbox. The sandbox is essentially a small area within your iDevice where the code can play freely. It is not allowed to play anywhere else. Hence the term Sandbox.
Because of the sandbox, it is very difficult to do simple things like uploading images to the web. There is no easy or convenient way to do this from email clients, Safari or other web browsers. There are no "upload" buttons.
This is because the sandbox isolates things; most applications simply cannot access other areas of the file system. Bad programs have a difficult time interacting with essential parts of iOS.
The sandbox is one of the reasons people have less to worry about. Is it infallible? No, I am betting some clever person will find a way to create issues. Or perhaps they never will because of iOS limitations.
If you are jailbroken, things can be/could be/are likely different. Jailbreaking exposes the iDevice file system so it can be accessed and manipulated in ways Apple does not allow. So jailbreakers must take steps. We are in the minority, however.