The right of visitation quoted by many Brothers is the 14th Landmark in Albert Mackey's Twenty-five Ancient Landmarks. Let us remember that not all Grand Lodges universally accepted those Landmarks as some adopted portion thereof, while others adopted all. Albert Pike challenged Mackey’s assertion and pointed out that no one can visit a Lodge without being vouched for and without the permission of the Master of the Lodge.
Though this is hard to say but this is another example of Masonic urban legend along with no one was ever invited to join our Craft. With numerous volume of books written, one have to show that Bro General Douglas MacArthur asked to be made Mason-on-sight. The same could be said about the long line of UK Royal family who traditionally held the Grand Mastership of both "Moderns" and "Antients” of GLE in their initiative to petition for Degress in Masonry. Let us face it, the "privilege" was offered and accepted for the benefit of both parties. In recent book by Walther Isaacson, Benjamin Franklin, an American Life, our esteemed Brother had to be "creative" to be invited to join in 1730. Asking one to be one is an American tradition/invention. The Continental and until recently English Freemasonry was almost exclusively by invitation only.
In UGLE website, their membership pitch did not say anything about adopting 2B1ASK1 and for clarification I did not hinted either. Postings from various Grand Lodges, from Singapore, Australia, South Africa, New Zealand and even Lodge in Wales consistently mentioned of stories of well to do gentlemen of being invited to join the Craft. And as I mentioned earlier of a recent book regarding Ben Franklin's desire to be invited to the Craft in 1730. As of 2002 UGLE website advised any interested person to contact a Brother who will invite him for a chat and if the Lodge is interested, he will get his petition and so on and so forth.
We know that at least in 1730 Freemasonry in States was by invitation and I could only speculate that probably after American Revolution that asking one to be one became practice. Let us be reminded that the Grand Lodge of Pennsylvania or New York did not asked UGLE's permission to be a separate/independent Grand Lodge. One could postulate that the new republic wanted to be seen as different and more egalitarian than English brand of Freemasonry. Interesting trivia were that 33 or 46% of American forces Generals were Masons, some were from same Lodges, all State Governors were Masons when Washington laid the cornerstone of either White House or Capitol according to some writings I read sometime ago.
As to the question of Washington as a Grand Master, in The Temple and Lodge by Beigent and Leigh, the same author who wrote the Holy Blood Holy Grail which, was the basis of Dan Brown's DaVinci Code, mentioned that Washington was offered to be the Grand Master of all Grand Lodges in America but declined thus keeping the current structure of independent Grand Lodges in every State. One could speculate that if Washington agreed then probably he will also agree to be the crowned King of America as some writings revealed as sidelight of American Revolution. Our worthy Brother truly exemplified one of the traits of a Past Master---wisdom. Now there was prime example of Masonic wisdom.