The point is, footballers all sign a clause when they register with the FA to say that they won't place ANY bets on football (regardless of whether it's to do with their team or not) and they won't do anything to influence a bet. Whether or not the bet is to do with a goal, full-time result or cramming a pie in your gob, it's all the same - the FA's stated opinion is that footballers are role-models and the slightest infringement or incident which could be seen as casting the game or its players in a negative light is unacceptable and must be punished.
It might sound like a bit of fun, but the thing you have to consider is that the FA will be looking at worst-case scenarios, and it may seem unlikely but a professional footballer is in the position of being able to arrange deals with big gamblers. One bookie has already announced (as I said above? can't be bothered to check) that they made a five-figure payout on the outcome. What if it were to come out that he had agreed to receive a quarter of the payout from a gambler he knew would put £5,000 on it? At the end of the day, we can't be sure that that didn't actually even happen...
I agree it's crazy and seems an overreaction, but that's the situation you have to deal with. It also starts to seem like less of an overreaction when you hear that there are rumours that match-fixers in South-East Asian countries routinely target English non-league games for seemingly innocuous bets such as whether certain players will get injured or whether there will be a corner in the Xth minute, because they are cheap to fix and because the level of information required to making the bets is available where it isn't anywhere else in the world. When you realise the amount of resources the FA has to put into chasing ghosts like that, you start to appreciate why they tend to come down like a ton of bricks on someone who visibly does something like this.