For me, the key issue would be tracking -- someone clicks from my web site to a referral site and then to a rehab-center web site, where they submit a lead form (or much more likely, call a toll-free number). The actual transaction is done "in person" at the facility.
Even if you design your tracking system well, patient confidentiality would almost certainly prevent any meaningful auditing; indeed, even if I knew that my cousin clicked on my link before submitting a lead form and then checked into Cozy Acres Rehab Center, and complained when I didn't get my referral fee, I doubt that you could even verify or deny that my cousin was treated there.
Also, to the extent that treatment is covered by insurance
or by government payments, I believe there are legal restrictions on paying referral fees or commissions based on transactions, similar to those for
ion medications. There may also be restrictions on paying referral fees for certain services (as a California attorney, I am barred from paying ANY referral fees to non-attorneys; I assume there are similar laws and regulations affecting medical professionals).