As far as I can tell, it is very unlikely IR interference will be a problem as long as the teams have remotes from different model TV/VCRs. Each IR signal is made up of 4 parts: a start command, the command itself, a device code (identifying the device to control by a certain binary number), and a stop command.
Check out this site:
http://electronics.howstuffworks.com...e-control2.htm
It has a good explanation as to how IR signals are transmitted.