I think that this intent issue matters at all only because if the intent was to pay ransom, then there is likely to be more kidnappings. That is why we have a policy against paying ransom. We don't want to encourage future kidnappings.
Therefore, it is the intent of the payor that matters. Only the payor can pay future ransoms. The payee cannot pay future ransoms.
In other words, if I am considering whether I should kidnap Americans for ransom next week, I care only about the payor's attitude about paying ransom. What another kidnapper might think is irrelevant to my decision.
For those kidnapped in furtherance of collecing on a claim might be freed, but never by payment of ransom.