This was an early animated prototype of Stanley Kubrick's "A Clockwork Orange" (which, btw, was released not in the late '60s, but in the early70s, and coincidentally it was the first of his pernament Warner Bros.Studio association!)
Other toons used this gimmick too. MGM's "Pipe Dreams" Warner's own "Wholly Smoke" Art Clokey's "Grub Grabber Gumby!"
Billy Bletcher was the villain, the very obscure Bernice Hansen, the little pig. The title was the only thing from that 1905 E.P.Butlerbook,"Pigs is Pigs", with a very different storyline than the WB cartoon, but Disney made a film twenty years later of the Butler book. WB was indeed the most cynical of the studios till Jay Ward,Hanna Barbera, then Spumco in the 90s.
Soundtrack includes "Fella with a Fiddle" and "When My Dreaboat Comes Home", also much used in WB shorts of the time-"Fella" in "The Cat Came Back", "The Blow-Out",the title short "Fella", and "Little Beau Porky",and "Dreamboat" in "Porky's Badtime Story", and its remake "Tick Tock Tuckered",and "The Birth of a Notion".
When the mother pig (talking in a Jewish accent--VERY sneaky WB type joke even for that un-PC period!) (as we see the outside shot of the piggie house!) warns her sonny-boy of indigestion, WE know he might have some nightmare, especially when he finds himself in a different place all of a sudden, especially when a Billy Bletcher-voiced mad doctor appears! But is it a dream, reality, or is it Memorex?
(Compare this with PORKY's shorts, or more recent live action comedies about fatness--"Big Momma's House 1 and 2", and this year's smashes "Norbit" and "Hairspray"! (and that last was set back in the sixties..)
The ending, like the "A Clockwork Orange" gimmick,is like "Wholly Smoke" (same director,Frank Tash), which DID have Porky.