My guess is the grandparent is (mis-)remembering the kerfuffle[0] around mongo shipping a copy of PG as a "BI Connector". But yeah, the timeline is off, that was in 2015.
Actually, no. I'm remembering asking myself how Mongo worked back when it launched, and reading somewhere that it was a heavily modded Postgres under the hood (like Amazon Redshift, which makes no secret about it, since).
I might be misremembering, though. And there's a possibility that what I read then was inaccurate.
I might admittedly be remembering this wrong, but I seem to recollect that Postgres had a couple of (unofficial) contrib modules to support JSON back in 2008 or so, and that (unfortunately buried in Postgres vs Mongo articles) the initial release of Mongo was actually a fork of Postgres for all practical intents.
The relevant data structures and indexing mechanisms (hstore, tsvector, gin, gist) were all available -- if only experimentally -- before Mongo launched.
I don't see how Mongo was built based on Postgres, either?