In my opinion as from an employer perspective....
If you left on good terms, I would ask you to do me a favor AND I would offer small financial incentive. (This is how I would do it only if I would ever do this in the first place--which I wouldn't).
I cannot believe a service is so hard up for cash that they would bother you over a few rejected payment claims and then reach out in an attempt to have you fix them so they can capture that revenue!! This is insane business practice to me.
From a legal perspective...you would have to ask a lawyer and I can only say I have never heard of such a legal obligation. You provided care, you documented it, you handed over care....this is a matter of them not getting paid for the work you did, not a matter of bad or inappropriate care.
From ethical perspective...again, all up to you. Would I appreciate a former employee willing to do this to help me capture lost revenue? Sure I would, however I am VERY cautious about what it is exactly they want you to write which will change the payment denial. It would most likely be in your best interest to NOT entertain the thought of assisting them because if you wrote a decent care report based on what you saw and did at the time and it still got rejected for payment...then I would be very skeptical of what it is they want you to "add" which would help the situation. You may find yourself participating in some illegal fraud all out of a sense of good will to a former employer.
They need to suck it up, write it off as a loss and move on.