Is there any environmental factor that could affect the thoughts of multiple people without being detected in an obvious way? Its detection could be analogous to blindsight. http://en.wikipedia.org/wiki/Blindsight
Maybe it would be a high or low wavelength of sound or light.
If this factor affects the thoughts of multiple people, a person might detect its influence on their own thoughts before they detect changes in the behaviors of those around them, and such a person might assume they have influenced the thoughts of others. Of course, they would not really be telepathic, thus they would be unable to recreate such an "effect" on command.
Tell me, have I been drinking too much caffeine? If the argument is relying on too many unsubstantiated premises, point them out.