Did the Beatles really Invent Prog? Or not?

You muppet. At that time double 'A' sides were counted as two separate singles, so what you failed to observe is that when you add the sales from Penny Lane, (which reached number one in the US chart and number two in the UK chart), it sold twice as many copies than the single that beat it to the top of the UK chart. This was not 'obviously "strange"' for everybody's ears since it was as successful as any other Beatles single at the time. Remember also that two weeks earlier The Move reached the very same number two in the UK chart with the Tchaikovsky inspired Night Of Fear, signifying that the British public were quite comfortable with a bit of Classical with their Pop. What this all was called of course, was Baroque Pop, and it was by no means a new genre, having been in existence for at least three years before SFF/PL was released. Sure Symphonic Rock was a derivative of Baroque Pop (among other things) but a hell of a lot of development ensued before Symphonic Rock became recognisable as a distinctly separated subgenre of Rock music.

 

Regarding Psychedelic and Baroque pop the tags, both tags are not quite suitable for Strawberry Fields Forever. Tomorow Never Knows is the great psych, and we could even describe that one as 'progressive psychedelia' aswell, but it's a 'psychedelic experience', not that haunting, pastoral and moony atmosphere of Strawbery Fields Forever.

The Beatles' songs like Yesterday and (or) Eleanor Rigby, simply due to that usage of the strings, were called Baroque pop. By the other bands, as an example of Baroque pop, I'd like to mention Walk Away Renee (1966) by NYC band The Left Banke. So everybody can hear that Baroque pop have nothing to do with Strawberry Fields Forever, i.e. SFF is not something derived from Baroque pop.

In lack of the term 'Symphonic rock' that will be coined some years later, Strawberry Fields Forever used to be and still to be wrongly tagged as a "Psych" and "Baroque pop", although both tags never ever work well for Strawberry Fields Forever  because Strawberry Fields Forever  already was something else, a new subgenre; The Beatles were move ahead. 

And that's it. Just born English Symphonic rock.