I can see no reason to doubt McCartney played that song when he met with Brian in April '67.
I've read that the song was A Day in the Life, played in the studio booth- presumably on cassette tape or acetate- and that he played She's leaving home, live. And that Brian played Paul Wonderful on the piano - source Derek Taylor.
Yeah, that's what I heard too. It was while they were recording "vegatables" too so Brian felt kind of embarassed that Paul brought him two amazing songs and he was diddling around with something that sounded silly.
Personally though, I doubt Paul took it that way because the Beatles were about to embark on plenty of silly music themselves.