Does a Bitcoin node need to scan through the whole blockchain in order to be 100% sure that a transaction sent to it is genuine? Does a Bitcoin node need to scan through the whole blockchain in order to be 100% sure that a transaction sent to it is genuine (especially when some inputs are derived from coins generated in the very early days)?
Yes. It doesn't have to do all the work when it receives the transaction, of course. If it's in sync with the network, it's already scanned the whole blockchain.