No. Point 4 is incorrect. Each node records in stable storage that it was able to commit or rollback the transaction, so that it will be able to do as commanded even across crashes. When the crashed node comes back up, it must realize that it has a transaction in pre-commit state, reinstate any relevant locks or other controls, and then attempt to contact the coordinator site to collect the status of the transaction.
The problems only occur if the crashed node never comes back up (then everything else thinks the transaction was OK, or will be when the crashed node comes back).