Is Sgt Pepper Prog?

There were literally thousands of progressive albums being made before either Sgt Pepper and Pet Sounds...but like those they too weren't rock albums. 

When we talk about prog rock I think we need to remember the rock part of the equation...or else we're back to the likes of Stravinski, Stockhausen, Coltrane, Charlie Parker and Ligeti who all made progressive albums before The Beatles and The Beach Boys. 

All of the above mentioned artists influenced prog rock on a wide scale, but that does not make them prog either. 

Quite right. But I apologize for derailing the train of thought that was off-track and soon as the OP left the station.

*Cues up "Locomotive Breath"*

In any case, I believe Sgt. Pepper's was "progressive" for the time without being "prog" per se. Juxtaposing a jaunty little McCartney ditty about personal hygiene in the middle of a surreal Lennon composition about the death of a beer baron's son isn't necessarily "prog". What the Beatles did in both Revolver and Sgt. Pepper's was to bring pop music to a level hitherto unknown to the people of this area (but destined to take the place of Chuck Berry in rock mythology).

The recording techniques and innovations they brought to the studio made possible albums like In the Court of the Crimson King and Dark Side of the Moon. It's safe to say Sgt. Pepper's brought a recording revolution to the studio that influenced Hendrix, Robert Fripp, Alan Parsons, and even Brian Wilson, who was driven mad just trying to keep up. The Beatles contribution to World Music (and I would suggest "Within You Without You" was revolutionary in that Harrison actually adhered to Hindustani classical music modes and scales in the composition, rather than just throw in a sitar and tabla for effect), and the later prog use of mellotron, tape loops and eccentric instrumentation (harmonium and glockenspiel!) found in "Being for the Benefit of Mr. Kite" and "Strawberry Fields Forever", was cause enough for a whole generation of prog rock musicians to be indebted.

People often say that....I simply don't get it. 

Any of those mentioned above...Days of Future Past....Procol's first ....The Nice-Ars ...all could qualify......but ITCOTCK will always be the one in my mind that started the prog craze.

They didn't have Mellotrons, either. 

Sgt Peppers?.. yeah maybe..  but in my mind the obvious album and group that one could argue persuasively, passionately AND intelligently both for and against would be the Moodies and Days of Future Passed. Much more than anything the Beatles did or the Beach Boys.. that was was closest if not squarely within the realm of what would soon be known as prog rock and the benchmarks which very quickly came to define it.. and it was fusing rock and European classical music.

let's not forget what prog was about boys and girls.. and frankly.. studio improvements aside...  neither did what Brubeck did in 1959.  Create what we associate MUSICALLY to be prog. Metric complexity, atypical arrangements, fearsome virtuosity, and diverse influence...

Nope, Zappa, The Nice and King Crimson where prog before there was prog. The Beatles where still pop rock on Sgt Pepper