The chat profile for a user includes a reputation total. This appears to be the sum of the reputation from all sites. A few days ago I logged in to a few other sites just out of curiosity, grew my chat reputation by 1k.
Given that there are 84 sites in the network, it seems like a person could get 200 rep on one site, and then login every single site in the network, and they would get 8,500 reputation points on chat (200+83*100).
This can be somewhat deceptive on chat when you see some with what appears to be a large reputation, and then find that they have used the site hardly at all. Reputation is intended as a measurement of helpful participation. If you include the account association bonuses, in a network-wide calculation, then I don't think it reflects participation very well.
This is slightly concerning because it appears that chat privileges is based purely on the total reputation. (I could be mistaken/wrong, I haven't anything on meta that contractions this assumption though). It seems like a person could get to a point where they can deal with flags by just getting a small amount of rep on a few sites. If my understand is correct, I do wonder if the chat reputation should be based on having 1k, or 10k on a single site, instead of having a total rep of 1k or 10k on all of the sites combined.