Sorry, the sites you listed are just opinion sites, there is no proof there. YOU have been deceived. There are many false prophets.
The author displays his lack of knowledge from the bat. The Jesus Prayer as practiced to this day in Eastern Orthodoxy is _not the same as mantras used in Eastern practice. It can be _mis-used_ and turned into a mantra, but any practice can be misused. Calling out to Jesus Christ our God for help and confessing one's sinfulness from the heart (the whole point of the Jesus Prayer) is very different from Buddhist ideas. Certainly, there are external similarities to Buddhism, in this and other ancient (and not so ancient!) Christian mystical practices, but they are by no means the same. Christian spirituality has as its heart the Incarnate God.
Incidentally, I found the reference to the Desert Fathers in The Purpose Driven Life very heartening and rather surprising.