Cooldoc80, it is not a myth! lol. If you use your logic a little bit, you will realise that it is a legitimate and sensible claim.
This is a very sensitive issue and has been touched and discussed so many times. You probably won't get the answer you are looking for that easily on this forum.
Until a few years ago, refugees used to be able to travel back and forth to their home countries as soon as they became permanent residents. That is because there was no legal immigration clause prohibiting them from doing so. However, the law has changed and the immigration authorities clearly advise refugees not to do that. Here is the link to the USCIS fact sheet about this:
http://www.uscis.gov/files/pressrelease/AsylumTravel122706FS.pdf
As you can see it clearly states that: "Returning to one’s country of claimed persecution may be relevant to a number of termination grounds. For instance, asylum status could be terminated based on a fundamental change in circumstances in the asylee’s country of persecution. Termination could also occur due to fraud in the asylum application such that the asylee was not eligible for asylum. Return to the country of feared persecution can, in some circumstances, be considered evidence that the asylee’s alleged fear of persecution is not genuine. In addition, termination of asylum status could occur if an “alien has voluntarily availed himself or herself of the protection of the alien’s country of nationality . . . by returning to such country with permanent resident status or the reasonable possibility of obtaining such status with the same rights and obligations pertaining to other permanent residents of that country. Accordingly, an asylee or a lawful permanent resident who obtained such status based on a grant of asylum status may be questioned about why he or she was able to return to the country of claimed persecution and, in some circumstances, may be subject to proceedings to terminate asylum status."
So you see, they strongly advise refugees not to do that and in case you do it, it can lead to many termination grounds. You will be questioned about it and if your story is not convincing enough, which most of the time it isn't, your asylum case will be terminated and you will be deported back to your country of claimed persecution, which is what happens most of the time. In your case, I am getting the feeling that you won't have a convincing story since you mentioned that: "... stay there for a year or so (of course i will come and go to states each 6 months)" and your case will most probably get denied.
If you are a Derivative Asylee, that is a totally different story. I believe that they can travel to COP with no problem because they are not the principal asylees and unless they will be persecuted directly in COP, they should be able to travel freely and if questioned about it, have a convincing story.
When you become a US Citizen, however, this whole thing completely changes. They still have not change the law and once you become a USC, you can travel back and forth whenever you want. But again, that really depends on how serious your persecution claim was, if it was legitimate, and if you really will be persecuted in your COP if you go there.
Any other opinions regarding this matter?