If you actually mean invalid signature/non-existent UTXO when you say "fake", it's impossible since each node verify the transaction before it's being shared with other node.
My technical knowledge is very basic but no, I wasn't thinking about that.
What I think is: suppose I have a coffee shop and I decide to accept bitcoin for coffee payments (let's leave aside LN), but I will accept the payment as good as soon as I see that the transaction is retransmitted to the blockchan. How likely is it that someone will slip me a transaction that is won't be not confirmed (and that doesn't have a very low fee, which I could check and reject the transaction based on that).