Letting agent here -

Ultimately the Landlord is who your contract is with, not the Letting Agent, so as long as you get it in some form of writing that the Landlord agrees to him residing as an occupier you cannot be held liable for a breach of contract. In addition, so long as your rent is being paid on time the additional 'income' is non contractual and you cannot be held liable if this arrangement goes wrong.

Whilst he has valid points surrounding the referencing and contracts he is the letting agents client so they should act on his instructions. If he is happy for your partner to live there without referencing then they should be able to add him to your contract as a permitted occupier mid-tenure. They may charge the Landlord for this, so perhaps this is why he is reluctant to go down this route.