Standing near and touching the radio probably represent two different phenomena.
In addition to traveling from one point to another, radio waves are being reflected and absorbed by objects in a room, and the pattern of reflection can cause interference as the spurious signal interferes with the original signal.
Standing in the path of the unwanted reflection can change the pattern at the antenna and improve the reception of the desired signal.
Only a tiny amount of the signal may be affected, but that can be enough to improve reception.
A good radio receiver can distinguish between the primary signal and the weaker reflected signal and reject the unwanted reflection.
On the other hand, by touching the radio, you really are being an antenna.
The body is filled with salt water, which is not a terrific conductor of electricity, but does conduct it.