The tooltip that comes up when you mouse-over the
flag for moderator option in chat is:
Moderator flags are only seen by the site-moderators, and should be used to indicate serious issues with a message, and other administrative issues.
When I read this, I interpret "site-moderators" as "the moderators of the site this chat room is associated with," for the following reasons:
"Site" sounds like "site-specific," and "only" also points in the direction of specificity.
Flags of content on an SE site are only seen by that site's moderators (and SE staff).
I tend to think of a chat room as an extension of the site it's associated with.
However, in this context, "site-moderators" actually means "the set of all people who are moderators on any SE site." I understand that the reason for this broadness is so that issues in chat can be handled quickly before they get too heated up, and a particular site's moderators may be all absent from chat at some times.
Consequently, some people who read this tool-tip may put information into such a flag that they would be comfortable sharing with their own site's moderators (and bothering them about) but not with the much-larger universe of SE site moderators.
I therefore suggest the following rewording, or something similar:
Moderator flags are seen by all Stack Exchange site-moderators who are using Stack Exchange chat right now, and should be used to indicate serious issues with a message, and other administrative issues.