Which band IS really America's Greatest (rock & roll band)?

Based on the above, I’d probably say NRBQ as well. I don’t think of bands like Grand Funk or The Eagles as ’rock and roll’ in the narrow sense of it-and much as I enjoyed The Band, Traffic and some of the others mentioned, I don’t think they are American (though The Band did a great job at the homespun Americana sound before it was re-booted as a genre).
If we aren’t confining ourselves to American bands, listen to The Beatles early on-- that concert at the Washington Coliseum is almost all pure old ’50s style rock and roll, great harmonies and playing under circumstances that would excuse most bands from a bad performance, and that was anything but.

@n80- not to be picayune, but I generally don’t refer to Canada as America, even though we are on the same continent. The Band were great, love ’em.
To me, rock and roll is the stuff that came out of the ’50s as a mix of boogie, country, blues and other forms- represented by that long list of notable performers from the era. I think that it pretty much died by the time the Eagles came around; their first two albums, which were country rock, were good- then, they became a sort of stadium rock act.
None of it was rock and roll in the narrow sense that I’m talking about- Jerry Lee Lewis, Live at Hamburg, for example, is a mind blower--not released here in the States at the time due to his PR problems with marrying his young cousin.
Some of the bands mentioned (though not necessarily American) did dive into rock and roll on occasion, but acts like the Beatles (who did r/r covers early on) and the Stones (no matter how much they ’rock’) weren’t in my estimation, mainly "rock and roll."
If the question is best rock band, different answer.
But, you know like I do there is no ’best.’ Today, I spent time listening to "Barbed Wired Sandwich," Black Cat Bones, a precursor to the band Free-- delicious, biting blues rock. Love it, but it ain’t "rock and roll" to me.
Bill

@n80- one thing with genres is that anybody who is innovating is gonna break the boundaries. The genre labels are like the Hollywood pitch summaries- 'it's like Die Hard Meets the Terminator on the Titanic"-- sort of sums it up, but puts it in a box. :)
I like a lot of very hard, post-psych stuff, and precursor bands-- but melody is pretty important to me. Rock and roll is very rhythmic - ke-chunk, ke-chunk, often drives it. Love hearing bands with a double bass--kind of emblematic of the early era. In terms of "best"- i leave that to those who do the listening- everybody's taste is different. Somebody with an overwhelming skill set can bore the life out of me; and somebody who doesn't have great technical skill (read Leslie West) can pull the soul out of notes.