Although I'm not sure if it's documented anywhere, it has been generally disclosed to users in the past that mods have the ability to enter any room in VRChat invisibly. If this is still the case, it seems like a reasonable moderation tool for public and friends+ rooms. It is also reasonable for mods to have access of entry to any and all rooms in VRChat.
However, if a room is set to private, the ability of a moderator to be invisible there is inappropriate. There are plenty of situations in which users would want to ensure that their interactions and conversation are truly private. It is in the users' best interests therefore for all users in an invite-only private space to know if an additional listening ear or observing eye is in the room. This could be handled either by disallowing invisibility, or with some visual indicator that an invisible user is present.
This will allow users to ensure that their interactions are confidential when they want them to be, and give them the choice to select what information they want to disclose based on the parties they know are listening. This measure of privacy would be in the user's best interests and would facilitate VRChat's role as a trusted platform for the community and its interactions.