Has science falsified prayer?

Atheists sometimes take the position that the efficacy of prayer has been scientifically disproven. The Benson Study is an oft-cited example.

Ironically, apostate Hector Avalos has torpedoed this objection by admitting that there’s no way to scientifically screen out prayer as a factor in the outcome:

The problem with this and any so-called controlled experiment regarding prayer is that there can be no such thing as a controlled experiment concerning prayer. You can never divide people into groups that received prayer and those that did not. The main reason is that there is no way to know that someone did not receive prayer. How would anyone know that some distant relative was not praying for a member of the group that Byrd had identified as having received no prayer? How does one control for prayers said on behalf of all the sick people in the world? How does one assess the degree of faith in patients that are too sick to be interviewed or in the persons performing the prayers? Even Byrd acknowledges these problems and admits that "'pure' groups were not attained in this study." [8] Since control groups are not possible, such purported scientific experiments are not possible.

http://www.secularhumanism.org/library/fi/avalos_17_3.html