I havent really ever put much thought into this. I used to get 1 captain to toss, 1 to call. More recently I just get away team to call. However, the lotg gives no direction as to who calls, it just says the referee tosses a coin. Therefore its starting to seem to me that nobody has a choice and the referee should allocate a coin side and toss it.
Probably thinking about this way too much.
Have you got a location of where you found that the referee tosses the coin in the LOTG? Just had a look but I could only find references to the winner, not the toss taker