It is very odd that you are the only Buddy this happens to for them.
In their iChat they should go to the View Menu and then Messages.
Then change the style from Balloons to anything else.
Between you check the colour of the Font you use and the colour of the IM background (whether you are using Balloons or not) and check this with the colour and background set at the other end for Incoming Overrides.
It is possible that they have changed one colour such as the Font one and it matches the colour of the Balloon/Background. (or vice versa). Most likely they have set Random colours ready for Group chats/Chatrooms and have set a Font Colour that becomes "Invisible")
It may pay for them to delete com.apple.ichat.plist found in their Home Folder/Library/Preferences (drag it to the Trash) and then Restart iChat.
This will unfortunately also lose all their other settings in the iChat Preferences.
Finally if none of these work they will have to Reinstall iChat.
This involves their Start Up Disk and downloading and Installing the COMBO version of the last OS Update they did (to re-update iChat)
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb( 10.6.7)
Mac OS X (10.6.7),
"Limit the Logs to the Bits above Binary Images." No, Seriously