I know that, at least in Tennessee, that is not the way it works. As a member of the Grand Lodge of Tennessee, I am subject to their rules wherever I am. Your suggestions do not hold up. If I were to go to WI, where PHA is recognized, I could not visit a PHA lodge. I am only subject to the rules of the GL that I am a member of. Otherwise, if what you said was true, it would make for a sticky situation when I travel to France. There are many Grand Lodges in France, most of which my Grand Lodge does not recognize. If what you said was true, I would simultaneously be under the jurisdiction of every GL in France and therefore be breaking rules no matter what I did.
Additionally, from what your Lodge website says I can see that you are not a member of a regular and recognized GL. But, if what you said in the above statement was true, you are currently under the jurisdiction of the Grand Lodge of Illinois. Therefore, by being a member in your "lodge" you are breaking their rules.
I would suggest that in the future you refrain from speaking for a system of Freemasonry that you claim to have no affiliation with, and apparently know little about.