In the end how do you feel about the relationship which seems to be a fledgling one. In the wider family circle is their children?
She has told you were she stands so if they wish to contact her then her response to the intrusion of her privacy and rights could be more devastating than her words to them.
I do not know her but she is possibly more worried about her family and friends finding out about your past and the effect that would have on her; especially as it is only a 'fledgling' relationship.
To protect herself she could tell her friends she ended it because of the offence then what would you do if you mingle in similar social circles.
I quoted a similar scenario whilst on licence and discussing the subject of disclosure and now to PPU. They always replied by silence or by the public protection statement.
In the end you protect yourself. As AB2014 says - let it ride and see what happens or as I would do, write to the PPU i.e. email and keep a copy, explain again her circumstances - no children, what you have said to her and her response. Then ask for their guidance and reasons they feel the disclosure is necessary given her circumstances i.e. do they want you end the relationship because of her rights to privacy? State this is so you can understand and so comply to their protection policies.
All PPU's handle situations differently and they are applying pressure on you. Once children become involved then you will also have social services involved. This unfortunately means this will not be end of the subject.
Be strong, believe in yourself and understand and act appropriately with any relationship.
Learn from yesterday, live for today, hope is for tomorrow else what is left if you remove a mans hope.