That is what you believe and if you were a prideful medical professional, that would also be your problem, not mine.
I know plenty of medical professionals who know God is the life-giver and they actually use prayer as part of their medical practice. Certainly, even an atheist EMT could be used to help someone in a serious situation, if God wanted them still here. And, God could still allow someone to die when a Christian EMT comes to an accident and administers medical help while also quietly praying for the person.
We can each believe what we want. God gives us that amazing freedom of choice. But, we also reap the consequences of a wrong choice. Whether I'm right or wrong, I look stupid to you in this life. And, that's okay to me. If your wrong, the penalty is much greater for you.
I also understand that the nerve (which causes sciatica) can certainly become unpinched. And, if we hadn't laid hands on the guy and watched God instantly take his pain away, then your point might be valid. But, given the immediacy of the healing right after the prayer, in this situation, your theory is the one that isn't backed by the evidence--but, then again, that is exactly what an atheist's theories usually are based on (a complete lack of evidence), so they need to make stuff up and reject the Truth no matter how undeniably likely.