You also have to have plenty of trust in the creators of the applications. Using Docker isn't really different, especially when the creators of the applications have also provided the Dockerfiles. What you had before Docker was just as much based on trust.
I have much more trust in the application developers. Thus, I'd trust first party docker images, but repackaged applicaton images would fall out of date more often and remain out of date for longer than most distro packages IMO. And, with distributions, there's a community of maintainers that try to package everything to a standard, with docker, I don't think that's the case.
