UTXOs cannot be spent twice, in the event of two competing transaction, the transaction which confirms first wins and the the other will be invalid.
The transaction isn't fake, but the coins were double-spend just as ranochigo explained here.
But the transaction was real, signed with the correct private key and broadcasted to the network.
Double spends are common, it can be done by mistake or it can be done under propose. Some people use them to cheat users, casinos and exchanges, and this is the main reason why we have to always wait for a confirmation. That's the only secure way we have to be secure that the coins will not be double spent.
I understand better now, thank you.