The registered keeper did in fact make representations and transferred liability to me as per my hire agreement.How do you know, have you seen their representations, evidence in support* and, crucially, the authority's Notice of Acceptance?
My point stands. On the basis of the PCN which does not categorise your standing they are demanding a penalty. Irrespective of the contravention their power to demand a penalty is subject to them complying with strict conditions and IMO it is open to you to put them to proof regarding their compliance, it's not for you to research. And if they do, then they should re-offer the discount.
Up to you.
*- vehicle-hire firm” has the meaning given in section 66(

of the Road Traffic Offenders Act 1988 (hired vehicles);
https://www.legislation.gov.uk/uksi/2000/2546/schedule/2/made“hiring agreement” has the meaning given in section 66(

of the Road Traffic Offenders Act 1988 (hired vehicles);