PostgreSQL natively indexes JSON data via the JSONB type.

True: as of 2019-12-24, released PostgreSQL versions supported indexing jsonb columns with built-in index types (e.g. GIN with jsonb_ops or jsonb_path_ops, or B-tree/expression indexes) and no third-party extension. Mostly true: native jsonb indexing existed but with a minor caveat in how it is described, e.g. it requires an explicit GIN index rather than happening automatically. Mixed or mostly false: indexing jsonb required extensions or worked only in limited ways. False: PostgreSQL had no jsonb type or no native way to index it at that date.

Set before the research began.

1. E1 8.14. JSON Types PostgreSQL Global Development Group (postgresql.org, PostgreSQL 11 documentation)

   “The default GIN operator class for jsonb supports queries with top-level key-exists operators ?, ?& and ?| operators and path/value-exists operator @>.”

2. E2 8.14. JSON Types PostgreSQL Global Development Group (postgresql.org, PostgreSQL 11 documentation)

   “The non-default GIN operator class jsonb_path_ops supports indexing the @> operator only. An example of creating an index with this operator class is:”

3. E3 8.14. JSON Types PostgreSQL Global Development Group (postgresql.org, PostgreSQL 11 documentation)

   “jsonb also supports btree and hash indexes. These are usually useful only if it's important to check equality of complete JSON documents.”

4. E4 Release 9.4 PostgreSQL Global Development Group (postgresql.org, release notes) · 18 December 2014

   “This new type allows faster access to values within a JSON document, and faster and more useful indexing of JSON columns.”

The PostgreSQL 9.4 release notes, dated 2014-12-18 (E4), introduced the jsonb type and describe "faster and more useful indexing of JSON columns". That was five years before the claim date. The PostgreSQL 11 documentation (E1–E3) describes built-in index support for jsonb: the default GIN operator class, the jsonb_path_ops GIN operator class, and btree and hash indexes. None of these needs a third-party extension. The user has to create these indexes explicitly, but the quote does not say indexing happens automatically, so the claim meets the criteria for true.