The entire point of partitions is that not all full nodes are validating (verifying) all transactions.
Thus of course the full node that wins a block (in PoW, and analogously ditto in PoS or consensus-by-betting) is trusting the validators of other partitions to not lie to him.
If that full node had to validate every transaction in every partition, then there wouldn't be partitions any more. The entire reason to make partitions is because verification costs are too high when every full node has to verify every transaction. Partitions exist to aid scaling.
Can we be clear on what you mean by validation? Validating a transaction (i.e. checking it is protocol valid) has no PoW cost associated with it, any full node can do this. Therefore any full node can reject an invalid transaction before it gets propagated around the network.