SQLite's HAVING clause picks an arbitrary row

Most SQL engines don't allow non-aggregate expressions in the HAVING clause. For instance, the Postgres docs state:

Each column referenced in condition must unambiguously reference a grouping column

SQLite, on the other hand, takes a surprising approach:

If a HAVING clause is a non-aggregate expression, it is evaluated with respect to an arbitrarily selected row from the group.

Perhaps this approach has precedence in other SQL implementations, but I would much prefer a hard fail over an arbitrary result.