The accepted answer is technically correct and probably alright for about 99% of all of the usual crop of Unix/Linux machines in use today, I assume. Still, we can tackle the problem with a slightly more differentiated view and try to target your actual question (which is not exactly "can root do everything in my machine" but "how can I protect myself").
@ceph3us linked https://security.stackexchange.com/questions/7801/keeping-secrets-from-root-on-linux in a comment. That question and its answers talks about possibilities to keep things secret from
root, available today. If you are real paranoid, and likely you will have to reinstall the machine, then you could try some of that stuff. I.e., SELinux with very restrictive settings.
SELinux has, in your scenario, a big drawback. The remote admins are remote admins because, well, they are supposed to admin your machine. This means they need to have full control over absolutely anything, to do basically anything with your machine, including making it secure in the first place. It is not a technical issue at all, it is one of organization. Even if you install SELinux, they will still need to have full access to do their job.
To transcend the question of
root, let's rephrase the problem like this: any remote admin who has enough power to do everything a remote admin needs to do (up to and including configuring and hardening any security aspects of the system) is outside of the security aspects of the system. By definition. No technical measure can change this, ever.
So, in practice, the only angle I see for you is this: reinstall the machine with your own installation, from scratch. Now, hear me out. There are two scenarios, both of which I have experienced in different companies: the one kind of company acknowledges that while most people (predominantly non-Unix people) could not care less, there are some people who are able and can be trusted to handle their own machine. If you are one of those guys, then you trade their potential service for your freedom. They usually will deny any help with your machine, after you took it over. Which is exactly what you want.
Then, you can harden it as much as you want, and your erstwhile admins will then have no particularly stronger possibility to hack your machine, compared to any other script kiddy out there.
This kind of company has understood that an internal LAN is not, by itself, a particularly safe place; i.e., it handles all machines on the LAN (even though they are presumably hardened by the company's team of admins) as possible attackers. In this scenario, they could care less about you installing your own stuff.
The other scenario is that your company simply forbids it. Then it's time to find out why that it the case. Are they afraid that you might botch your machine and then call them for help, which will be hard for them to do? Assure them that you will handle yourself. Is there a license issue? On Linux? Don't think so. Are they afraid that you can run malicious code/install stuff from the internet, whatever? You can already do that, you already have root. Do they think you can do the machine to do malicious stuff without their keyloggers/screenloggers seeing it? Then you probably work at the NSA and they monitor their own guys (I'm just kidding, I have no idea about NSA internals ;) ).
You see where I'm going, I hope. There is no practical reason to assume that you using their installation (with you having full root access yourself) makes anything safer than you using your own installation and them having no access.
Try to convince them, or find out why they won't be convinced. That should tell you something, maybe.