The false claims act is more relevant to misrepresentation of information on a claim, and where you can run into trouble is if practice is actually willing to accept a lower amount as payment in full for services than what you are stating are your charges on the claim form. It's questionable how that would apply to your particular situation since with a self-pay patient there is no claim involved. What you're describing is a provider performing an instance of charity care for an uninsured patient which is a little different. But you might want to take a look at this guidance from the OIG, there's a lot of good information here:
http://oig.hhs.gov/fraud/docs/alertsandbulletins/121994.html
About half-way down, it says: "When providers, practitioners or suppliers forgive financial obligations for reasons other than genuine financial hardship of the particular patient, they may be unlawfully inducing that patient to purchase items or services from them."
I think it's unlikely that you'd run into problems if these are isolated instances done with the intent of helping a patient who is in financial difficulty, especially if no government or commercial payer is involved, but to protect yourself the best approach is to have a written financial hardship policy and have some process in place to demonstrate that your practice is making an effort to collect payments and only forgiving charges in situations when there is a legitimate and verifiable hardship involved.
Hope this helps some.