I agree that a "2/4" game means the bets are in $2 units before the turn and $4 after the turn. However, the small blind is likely be $1. It sounds like when Arizona Charlie's is calling a game "2/4" they are referring to the blinds, which would mean a small blind of $2, and a big blind of $4, which would imply $8 bets after the turn. I've never heard this usage before so I don’t blame you for being surprised.
p.s. I later received the following from Anthony, a poker room supervisor.
I am a poker room supervisor. I was just writing to let you know about the correct wording for the poker limits in Texas Hold 'em. If as game is referred to as $2/4. It is referring to the bets. (A game is only referred to by the blinds if it is No-Limit.) $2 pre flop and post flop,$4 on the turn and the river.A game that is listed as $2/$4/$8 (which is exactly what I suspect the previous letter writer was actually referring to, is $2 pre-flop,$4 post-flop,$8 turn and river .It is also possible to have a game listed as $2/$4/$6/$8. Just passing the information on, good poker supervisors want people to have as much information as possible.