Is it simply a case of both the doctor and the specialist being awfully nice chaps who do not want you to be out of pocket?
Or is there something less than fragrant about the whole transaction?
A businessman from Essex (who cannot be named for legal reasons) was recently referred to a specialist by his local NHS doctor. The businessman, who we shall call Mr Jones, is insured with Bupa.
The medical section of the Bupa claim form has to be completed by 'the GP/specialist in charge of the treatment'.
A spokesman for Bupa said: 'Either the doctor or the specialist can sign. A specialist will consider it to be part of his services but a doctor will charge for it and the subscriber cannot claim it back.'
Mr Jones took his insurance claim form with him to the specialist. He says: 'The specialist referred me back to the doctor to sign the form.
'He told me the doctor would charge a fee for signing, but that if I got a receipt then the specialist would reimburse me.
'I thought it was a little odd at the time. But if someone is offering to pay you back money, then you hardly give him the third degree.'
Mr Jones went to his doctor and got the form signed. The doctor charged him pounds 12.50.
Mr Jones paid by cheque. He got his receipt, and sent it off to the specialist. He then went into hospital.
During one of the specialist's visits to his bedside, Mr Jones was handed an envelope. The envelope contained the specialist's personal cheque for pounds 12.50.
Mr Jones says: 'For some strange reason, everyone is swopping cheques. I cannot believe that I am the only person who is getting a refund in this way.'
Dr Sandy Macdonald-Smith, a director of Executive Health Care, an independent medical consultancy, says there may be a perfectly innocent explanation. However, it appears far more likely to him that the money is a backhander.
He explains: 'The specialist could have signed the form for free. Instead, he referred it back to the doctor who charges the fee, with the patient being used as the channel between them.
'The consultant is in effect rewarding the doctor for the referral.
'The whole practice is absolutely deplorable, and is frowned on by the medical profession.'
Julian Stainton, the managing director of medical fees insurer Western Provident Association, is equally perturbed at the financial antics of some members of the medical profession.
He says: 'Reimbursement may of course be explained away as excellent customer service for the patient, but to me it smacks of backhanders.
'And you can speculate that the consultants will not be out of pocket. They will probably somehow just 'lose' the amount they have paid in their bill.
'It raises a very large number of question marks over the financial relationship between doctors, consultants and private hospitals.'
Rumours abound that some private hospitals also may not be averse to a little sweetener to the family doctor.
There are said to have been instances of the payment of so- called administration charges - when doctors are reimbursed directly by the private hospital for signing medical insurance forms. There is particular concern about a hospital in Essex.
Mr Stainton says: 'There must be an immediate investigation into all these practices among doctors and hospitals. The patients are not out of pocket but it makes you wonder whether you are being referred to a particular specialist or hospital for medical or financial reasons.'
Meanwhile, if your insurer gives you the option to have your claim form signed by your doctor or specialist, then if cost-saving is paramount, plump for the specialist who will do it for free.
Bupa and Norwich Union give you the choice. Private Patients Plan insists in theory that the form is signed by a doctor.
But in practice, it says, 'we do accept them signed by a specialist'. Western Provident insists on a doctor's signature.