Is this true? You still need connections to the rest of the network so that you know your block chain is the longest one and you get the number of confirmations

Is this true? You still need connections to the rest of the network so that you know your block chain is the longest one and you get the number of confirmations that both of you feel is sufficient to remove double-spend risk. So it's not really just between the two of you, even if you both have full nodes. Right?