I am studying about Bitcoin and Blockchain tech via the Princeton crypto course, and it mentions that Full nodes do the following checks :
i)transaction is valid with the current blockchain,
ii)whether the scripts matches whitelist,
iii)transaction hasn't been seen before and
iv)doesn't conflict with others its relayed (to avoid double spend).
However, the lecturer also mentioned these checks are not enforced on a node. Lets say a full node may have a full set of of UTXO but still decides to relay a transaction that has been spent before (effectively ignoring the fact that the TX is not on the UTXO pool) , and eventually this TX is relayed around and makes it into a block. Since the miners trust these nodes to verify transactions , wouldn't the TX be put into the consensus chain ?
I understand that the mining process (POW) and resulting block reward can only be claimed/collected if the block ends up on the long-term consensus branch, but this doesn't safeguard the malicious node behavior as I have explained since miners don't check for double spends.