This entire answer is from the perspective of someone who was 15 when this album was released - right in the target audience at the time for such an album.
The joke is actually in the exaggeration, rather than the statement itself.
That everybody in the US received a free copy in the mail along with other spam is just part of that exaggeration.
Frampton Comes Alive! was a colossal international hit, yet appeared to come from nowhere. At the time no-one [of our age group, ref above] really knew who he was or where he came from. After a while we discovered he used to be in 'Humble Pie' & 'The Herd' but we weren't quite sure who they were either.
There was no Google in 1976.
And yes, at the time, it did seem that absolutely everybody had a copy. Even your parents would like it - which would ordinarily be a bad thing.
You would hear it played wherever you went; parties, supermarkets, every radio station... it became hard to get away from after a while.
It was possibly the world's first 'coffee table album' [complete opinion on my part, no evidence.]
For me "Show Me the Way" was the big breakthrough single from it.
From the first couple of paragraphs of the Wikipedia p[age...
Frampton Comes Alive! is a double live album by English rock musician
Peter Frampton released in 1976. It is one of the best-selling live
albums in the United States, and considered by many to be one of the
finest live rock recordings of all time. Following four solo albums
with little commercial success, Frampton Comes Alive! was a
breakthrough for the artist.
Released on January 6, 1976, it debuted on the charts at 191. The
album reached number one on the Billboard 200 the week ending April
10, 1976, and was in the top spot for a total of 10 weeks. It was the
best-selling album of 1976, selling over 8 million copies in the US
and becoming one of the best-selling live albums to date, with
estimated sales of 11 million worldwide.
Frampton Comes Alive! was voted "Album of the year" in the 1976
Rolling Stone readers poll. It stayed on the chart for 97 weeks and
was still No. 14 on Billboard's 1977 year-end album chart.
Personal opinion as to why it never had a famous follow-up... by 1977 the UK was ruled by Punk & no-one would even admit to owning Comes Alive any more, let alone buy the next one.