On Linux, sudo gives you domain rights so you can mess up your own machine, you can become any user on any machine.
Sounds like complete nonsense, until you "translate" it from the Windows mind-set from which it almost certainly emanated:
sudo gives you domain rights ...
This person is conflating "elevated permissions" with "domain rights" (whatever they might be) unless they've set up their "domain" in a very, very strange way - setting up root as as Domain User would be a huge security risk.
Yes, sudo lets you do things that you would not, normally, be allowed to, but it's still absolutely nothing to do with a "domain".
... you can become any user on any machine ...
Yes, you can "become" (through "sudo -i") any user on any machine ... on which sudo has been configured to allow you to do so, or on which sudo has been configured to allow you to "become" root (which can, by design, do anything, so all bets are off).
All that configuration is down to your System Administrators and how they've set up sudo. From the sounds of it, that's naively, lazily and/or poorly. YMMV.
I'm guessing that you have [your own] Windows desktops, but [shared] Linux servers.
Elevated permissions on your desktop machine allow you to shoot yourself in the foot by lousing up your own machine. I would guess that your organisation ("large corp with fairly strict IT") has standard, desktop "build" images that they can "splat" over your crippled machine to get you back into a working state.
sudo allows you to run commands as another user, most commonly as root, which allows you to shoot everybody in the foot (feet?) by lousing up a shared server, which then requires a System Administrator to take the time and trouble to step in and clean up your mess. This doesn't make you any friends.