Jerome, Thanks for the reply. I think you are refering to the Wrightnour book then, in which case, I am familiar with that reference. The problem with Wrightnour is that a number of things have never been proven -- which he also admits. A distant Frampton "cousin" and I have been re-doing Wrightnour's research and hoping to find the missing clues.
We have uncovered some new info not mentioned in the book, but no proof yet that William's son Thomas ever had a son named John and/or that John Frampton was really descended from either Thomas or William. As far as we can tell, Wrightnour's primary source was my ggggrandfather William Frampton (1803 - 1883) who presumably heard the story from John's son William II, who died in 1829, when William III would have already been 26 and so, in our opinion, old enough to have gotten the story straight. Still, it is only second-hand family tradition. However, as Wrightnour says, everything that William III told him that could be proven, checked out for 100%, so chances are that this family tradition is also correct.
Interesting is that in some family histories of other family members, Thomas is left out, and the decendants claim that John was the son of William, which is of course, physically impossible. Another point is that although William was active for about 3 years in the early PA government, his wife Elizabeth was probably even more interesting if you follow her life, but no one ever talks much about her.
As to your question on the Bishop, I haven't had time to fully transcribe his will, but from what I can see, it could be that he and William's father were brothers or that there was a relationship even one more generation removed, but this is not certain. His donation to Burlington was probably just a coincidence. Unfortunately, Quakers were often disowned (certainly by a Bishop & his relatives!) and also stricken from parish records, so we may not find anything on this one.
I take the time to write this because Wrightnour is so often quoted -- especially since internet research has gotten so widespread -- as the absolute truth and most people tend to jump over the fact that beyond John, the story is in part speculation. This also applies to the Critchfield - Opdyck story, although at least here, we have found evidence of the two families living in close proximity and also a very strong naming pattern in both the Critchfield and Frampton families.