Any Political Theological Relevance to the term the "Great Spirit"?

I got two important questions comments, first from reader Jim51 and second by Jim Goswick, aka Our Founding Truth. I think we all recognize the utility, when speaking to unconverted Natives, in terming God "The Great Spirit" as it speaks their language. Likewise those same Founding era Americans referred to George Washington as "The Great Chief" when talking to the Natives.

The QUESTION is whether the "Great Spirit" worshipping Natives really DO worship the same God as Christians. Under a very ecumenical (perhaps heterodox, perhaps not) understanding all monotheists (Jews, Christians, Muslims, Unitarians, Deists, at least the ones who believe in Providence) worship the same ONE God -- the God of the Bible.

But not everyone interprets the Bible this way. Conservative evangelical Jim Goswick writes:

His point is most likely to link Putnam with the other infidel framers: George Washington, and James Madison, who used the same term referring to the Indian "Great Spirit." I call them infidels because that is what they would be if they considered the Indian god--or any god--the same as the Biblical God. The Bible says at least one thousand times, He is the Only God, the God of the Israel.

Not only is Rowe's implication far-fetched, it would make George Washington a very ignorant man, given a Christian high schooler understands the difference. That Putnam and Washington are placating diplomatically to the Indians by referring to God in their terms is obvious--however Putnam was an Evangelical. The only reason an Evangelical would link the Indian Great Spirit with the God of the Bible is to be diplomatic and accomodating [sic].

I'm not sure if I quite get his point. Yes, I think we all understand the diplomacy and accommodation. And if all monotheists -- including Muslims and unconverted Native Americans -- worship the same God then we have an easy diplomatic and accommodating Truth. Goswick seems to suggest that unconverted Natives really DIDN'T worship the God of the Bible with men like Washington and Putnam in knowledge of this. What would that make them then? Manipulative hypocrites when dealing with Natives. Suggesting unconverted Natives worship the same God Christians do, while not believing it, reeks of the same charge of hypocrisy that some secular nationalist scholars make when they claim the early Presidents were cold deists (or atheists) who may have publicly spoken as though they believed in Providence or something closer to Christianity to placate the masses over whom they ruled.

Finally, about Rufus Putnam's personal religion. I know David Barton quotes Putnam's Will that has orthodox Christian like language. I haven't yet independently verified the quotation in reliable sources. But if true, it tells us precisely nothing of Putnam's religion when he did his "Great Spirit" talk with the Natives.