You say you were getting JSA and have confirmation that you were awarded "tax credits" for that period. Later you refer to "NI tax credits". I'm a little confused. Tax credits are nothing to do with JSA or NI. They are a quite separate matter, administered by HMRC (previously Inland Revenue).
Do you mean you have confirmation you were getting NI contributions credited? If so, then clearly the outcome of any Court case would have been different from what occurred because you would have been able to prove that you did not owe all of the money being claimed. In this case, it seems there could well be a good case for set aside, but there are no guarantees about how a judge will see it.
I don't know how the NI contributions system keeps its records but what you say seems perfectly logical to me. Presumably NI Contributions Record Centre will have been sent information via the Job Centre system that you were being credited with contributions, and this should have gone onto your record. If it did, they should not have billed you for that period; if it did not, then there appears to have been a fault in their records system somewhere.
As I said before, either pay what you owe before the Court hearing, or take the money to Court.