At which level in the sciences are you ever supposed to trust that your colleagues have done their work correctly? That sounds more like the opposite of what you are supposed to be doing.
Well before that, though, it becomes impractical to re-check every single thing. And the longer-established a field is, the more you have to take on faith.
A citation does generally mean that you hold a given paper with a certain level of trust, but that isn't the same as having trusted the people who wrote it to have done their job properly.
The trust in the paper could be because you trust the folk who wrote it to have gone and done their job properly, however the trust could also be from having actively gone and checked the working.