The answer is yes and no (note, in this blog, I'm not talking about cryptographic or identity trust, but systems trust). There are two aspects to this. Firstly, do you think your users will deliberately act against your organisation or try to harm the system? This is not usually the case for corporate employees - you also have severe sanctions available if they do. The second aspect is, do you trust your users NOT to make mistakes? Everyone makes mistakes; we're only human. You don't want accidental updates or changes, so in this sense maybe you shouldn't trust your users.
Actually there are three overall approaches to system trust on networks. We can trust all of the people all of the time (bad idea, but much more common than you'd think), trust no one at any time (maybe too excessive and hinder functionality), or we can trust some of the people some of the time. The last one is usually the best strategy to adopt for your network.
Finally, we have to decide on the overall approach to security. Are we permissive or restrictive? In a permissive environment you can do everything, apart from those things on a blacklist. In a restrictive environment, you can do nothing, apart from those things on a whitelist. From a security standpoint restrictive is better, but from a usability standpoint permissive is better. If you can manage the whitelist successfully, this is the better solution and only trust some of the users some of the time.