General Information: While the image does indeed resemble a giant eye, there is no record of NASA actually referring to it as "The Eye of God". It is not clear who first called the image "The Eye of God", but the name appears to have "stuck" for obvious reasons. A number of non-NASA websites refer to the image by this name. In fact, other planetary nebulas have also been called "The Eye of God", including the "Hourglass Nebula, MyCn18."
The "Helix Nebula" is actually a vast tunnel of glowing gases a trillion kilometres long. Since Earth's position in relation to the nebula means we are looking more or less directly into the mouth of this tunnel, the Helix appears to us as an eye-like bubble rather than a cylinder.
The claim that this "event" only occurs once in 3,000 years is pure nonsense. The "Helix Nebula" is readily viewable by scientists all the time and can even be seen by amateur astronomers using telescopes or binoculars. Naturally, due to the composite nature of the image and the high-powered telescopes and photographic equipment used to create it, the nebula is unlikely to look as compelling or as "eye-like" from the ground as it does in the above image.
In spite of the inaccurate description, the picture is certainly a delight to behold, both for the scientists (Cosmologists, Astronomers, et al) as well as for the amateurs. Awesome, indeed! Gives anyone who views this picture - a feeling, that - "God loves you and watches over you every day." We bow before Mother Nature in all humility.....again and again and again......
Note: Image Credit - NASA, WIYN, NOAO, ESA, Hubble Helix Nebula Team, M. Meixner (STScI), & T. A. Rector (NRAO). Information gathered from Wikipedia.