Checking non-EEA family members right to work

Hi there

Just wondering if anyone has had experience of a non-EEA national's employer checking his/her right to work by using the Employer Checking Service?

The reason why I'm asking is that my civil partner has already been given a job as a waiter and is getting paid quite well for it. However, the employer (whom I know through a friend) has not taken any copies of his EEA family permit nor even his passport. I know that the employer should complete the Employer Checking Service Enquiry Form. However, they don't seem to be interested in doing this. They just trust me. The form says:
["This form should only be completed where an employer is seeking to confirm the right to work of an employee or a prospective employee who has:
A ‘Certificate of Application’ issued to or for a family member of an EEA national stating that the holder is permitted to take employment which is less than 6 months old;
an Application Registration Card (ARC card) stating “Employment Permitted“ or “Allowed to work”"] (Parts deleted).

Is this gonna cause any problems for the company? I know it's my partner's right to work here in the UK (I'm an Irish citizen who holds EEA1 registration certificate issued by the Home Office). I know that this right exists as a I have an email from the European Operational Team within the Home Office.

Cheers for any ideas
CC