I worked in IT for about 15 years, and always held that if a company doesn't trust its network administrators for a justifiable reason, then those people shouldn't be the network admins.
Remote/local doesn't matter. If they are not trustworthy and you can document why, then don't make them your admins. If they are, then don't worry about it until they do something to violate that trust. And if they do violate that trust, then go after them guns a-blazing (figuratively, not literally, OBVIOUSLY).
Most network admins want to be trusted - and need to be. Being untrustworthy is the kiss of death in that entire career path.
As others have said, local or remote doesn't matter. In-house or outsourced doesn't really matter. You need to accurately assess their trustworthiness and then deal with it in an appropriate manner.